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MATHEMATICS (706 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 27)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 6)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 12)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 3)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 5)
Advances in Science and Research (ASR)     Open Access   (Followers: 4)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 10)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Archive for Mathematical Logic
  [SJR: 0.946]   [H-I: 23]   [2 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0665 - ISSN (Online) 0933-5846
   Published by Springer-Verlag Homepage  [2351 journals]
  • The tree property at the successor of a singular limit of measurable
    • Authors: Mohammad Golshani
      Pages: 3 - 25
      Abstract: Assume \(\lambda \) is a singular limit of \(\eta \) supercompact cardinals, where \(\eta \le \lambda \) is a limit ordinal. We present two methods for arranging the tree property to hold at \(\lambda ^{+}\) while making \(\lambda ^{+}\) the successor of the limit of the first \(\eta \) measurable cardinals. The first method is then used to get, from the same assumptions, the tree property at \(\aleph _{\eta ^2+1}\) with the failure of SCH at \(\aleph _{\eta ^2}\) . This extends results of Neeman and Sinapova. The second method is also used to get the tree property at the successor of an arbitrary singular cardinal, which extends some results of Magidor–Shelah, Neeman and Sinapova.
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-017-0581-4
      Issue No: Vol. 57, No. 1-2 (2018)
  • On a question of Silver about gap-two cardinal transfer principles
    • Authors: Mohammad Golshani; Shahram Mohsenipour
      Pages: 27 - 35
      Abstract: Assuming the existence of a Mahlo cardinal, we produce a generic extension of Gödel’s constructible universe L, in which the \(\textit{GCH}\) holds and the transfer principles \((\aleph _2, \aleph _0) \rightarrow (\aleph _3, \aleph _1)\) and \((\aleph _3, \aleph _1) \rightarrow (\aleph _2, \aleph _0)\) fail simultaneously. The result answers a question of Silver from 1971. We also extend our result to higher gaps.
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-017-0586-z
      Issue No: Vol. 57, No. 1-2 (2018)
  • On some dynamical aspects of NIP theories
    • Authors: Alireza Mofidi
      Pages: 37 - 71
      Abstract: We investigate some dynamical features of the actions of automorphisms in the context of model theory. We interpret a few notions such as compact systems, entropy and symbolic representations from the theory of dynamical systems in the realm of model theory. In this direction, we settle a number of characterizations of NIP theories in terms of dynamics of automorphisms and invariant measures. For example, it is shown that the property of NIP corresponds to the compactness property of some associated systems and also to the zero entropy property of automorphisms. These results give a correspondence between some notions of tameness in model theory and ergodic theory. Moreover, we study the concept of symbolic representation and consider it in some well known mathematical objects such as the circle group, Bohr sets, Sturmian sequences, the structure \((\mathbb {Z},+,U)\) , and random graphs with a model theoretic point of view in mind. We establish certain characterizations for stability theoretic dividing lines, such as independence property, order property and strict order property in terms of associated symbolic representations. At the end, we propose some applications of symbolic representations and these characterizations by giving a proof for a classical theorem by Shelah and also introducing some invariants associated to the types and elements of models.
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-017-0580-5
      Issue No: Vol. 57, No. 1-2 (2018)
  • The long extender algebra
    • Authors: Ralf Schindler
      Pages: 73 - 82
      Abstract: Generalizing Woodin’s extender algebra, cf. e.g. Steel (in: Kanamori (ed) Handbook of set theory, Springer, Berlin, 2010), we isolate the long extender algebra as a general version of Bukowský’s forcing, cf. Bukovský (Fundam Math 83:35–46, 1973), in the presence of a supercompact cardinal.
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-017-0585-0
      Issue No: Vol. 57, No. 1-2 (2018)
  • Aronszajn and Kurepa trees
    • Authors: James Cummings
      Pages: 83 - 90
      Abstract: Monroe Eskew (Tree properties on \(\omega _1\) and \(\omega _2\) , 2016. asked whether the tree property at \(\omega _2\) implies there is no Kurepa tree (as is the case in the Mitchell model, or under PFA). We prove that the tree property at \(\omega _2\) is consistent with the existence of \(\omega _1\) -trees with as many branches as desired.
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-017-0579-y
      Issue No: Vol. 57, No. 1-2 (2018)
  • Largest initial segments pointwise fixed by automorphisms of models of set
    • Authors: Ali Enayat; Matt Kaufmann; Zachiri McKenzie
      Pages: 91 - 139
      Abstract: Given a model \(\mathcal {M}\) of set theory, and a nontrivial automorphism j of \(\mathcal {M}\) , let \(\mathcal {I}_{\mathrm {fix}}(j)\) be the submodel of \(\mathcal {M}\) whose universe consists of elements m of \(\mathcal {M}\) such that \(j(x)=x\) for every x in the transitive closure of m (where the transitive closure of m is computed within \(\mathcal {M}\) ). Here we study the class \(\mathcal {C}\) of structures of the form \(\mathcal {I}_{\mathrm {fix}}(j)\) , where the ambient model \(\mathcal {M}\) satisfies a frugal yet robust fragment of \(\mathrm {ZFC}\) known as \(\mathrm {MOST}\) , and \(j(m)=m\) whenever m is a finite ordinal in the sense of \(\mathcal {M}.\) Our main achievement is the calculation of the theory of \(\mathcal {C}\) as precisely \(\mathrm {MOST+\Delta }_{0}^{\mathcal {P}}\) - \(\mathrm {Collection}\) . The following theorems encapsulate our principal results: Theorem A. Every structure in \(\mathcal {C}\) satisfies \(\mathrm {MOST+\Delta }_{0}^{\mathcal {P}}\) - \(\mathrm { Collection}\) . Theorem B. Each of the following three conditions is sufficient for a countable structure \(\mathcal {N}\) to be in \(\mathcal {C}\) : (a) \(\mathcal {N}\) is a transitive model of \(\mathrm {MOST+\Delta }_{0}^{\mathcal {P}}\) - \(\mathrm {Collection}\) . (b) \(\mathcal {N}\) is a recursively saturated model of \(\mathrm {MOST+\Delta }_{0}^{\mathcal {P}}\) -
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-017-0582-3
      Issue No: Vol. 57, No. 1-2 (2018)
  • The small index property for homogeneous models in AEC’s
    • Authors: Zaniar Ghadernezhad; Andrés Villaveces
      Pages: 141 - 157
      Abstract: We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah (in their case, for saturated models of uncountable first-order theories). We then study versions of the small index property for various non-elementary classes. In particular, we obtain the small index property for quasiminimal pregeometry structures.
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-017-0587-y
      Issue No: Vol. 57, No. 1-2 (2018)
  • Model theory of finite and pseudofinite groups
    • Authors: Dugald Macpherson
      Pages: 159 - 184
      Abstract: This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory.
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-017-0584-1
      Issue No: Vol. 57, No. 1-2 (2018)
  • Collapsing $$\omega _2$$ ω 2 with semi-proper forcing
    • Authors: Stevo Todorcevic
      Pages: 185 - 194
      Abstract: We examine the differences between three standard classes of forcing notions relative to the way they collapse the continuum. It turns out that proper and semi-proper posets behave differently in that respect from the class of posets that preserve stationary subsets of \(\omega _1\) .
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-017-0588-x
      Issue No: Vol. 57, No. 1-2 (2018)
  • Convexity and unique minimum points
    • Authors: Josef Berger; Gregor Svindland
      Abstract: We show constructively that every quasi-convex, uniformly continuous function \(f:C \rightarrow \mathbb {R}\) with at most one minimum point has a minimum point, where C is a convex compact subset of a finite dimensional normed space. Applications include a result on strictly quasi-convex functions, a supporting hyperplane theorem, and a short proof of the constructive fundamental theorem of approximation theory.
      PubDate: 2018-02-22
      DOI: 10.1007/s00153-018-0619-2
  • Diagonal reflections on squares
    • Authors: Gunter Fuchs
      Abstract: The effects of (bounded versions of) the forcing axioms \(\mathsf {SCFA}\) , \(\mathsf {PFA}\) and \(\mathsf {MM}\) on the failure of weak threaded square principles of the form \(\square (\lambda ,\kappa )\) are analyzed. To this end, a diagonal reflection principle, \(\mathsf {DSR}{\left( {<}\kappa ,S\right) }\) is introduced. It is shown that \(\mathsf {SCFA} \) implies \(\mathsf {DSR}{\left( \omega _1,S^\lambda _\omega \right) }\) , for all regular \(\lambda \ge \omega _2\) , and that \(\mathsf {DSR}{\left( \omega _1,S^\lambda _\omega \right) }\) implies the failure of \(\square (\lambda ,\omega _1)\) if \(\lambda >\omega _2\) , and it implies the failure of \(\square (\lambda ,\omega )\) if \(\lambda =\omega _2\) . It is also shown that this result is sharp. It is noted that \(\mathsf {MM}\) / \(\mathsf {PFA}\) imply the failure of \(\square (\lambda ,\omega _1)\) , for every regular \(\lambda >\omega _1\) , and that this result is sharp as well.
      PubDate: 2018-02-19
      DOI: 10.1007/s00153-018-0614-7
  • On partial disjunction properties of theories containing Peano arithmetic
    • Authors: Taishi Kurahashi
      Abstract: Let \(\varGamma \) be a class of formulas. We say that a theory T in classical logic has the \(\varGamma \) -disjunction property if for any \(\varGamma \) sentences \(\varphi \) and \(\psi \) , either \(T \vdash \varphi \) or \(T \vdash \psi \) whenever \(T \vdash \varphi \vee \psi \) . First, we characterize the \(\varGamma \) -disjunction property in terms of the notion of partial conservativity. Secondly, we prove a model theoretic characterization result for \(\varSigma _n\) -disjunction property. Thirdly, we investigate relationships between partial disjunction properties and several other properties of theories containing Peano arithmetic. Finally, we investigate unprovability of formalized partial disjunction properties.
      PubDate: 2018-02-14
      DOI: 10.1007/s00153-018-0618-3
  • A collection of topological Ramsey spaces of trees and their application
           to profinite graph theory
    • Authors: Yuan Yuan Zheng
      Abstract: We construct a collection of new topological Ramsey spaces of trees. It is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. We give an example of its application by proving a partition theorem for profinite graphs.
      PubDate: 2018-02-10
      DOI: 10.1007/s00153-018-0617-4
  • Splitting idempotents in a fibered setting
    • Authors: Ruggero Pagnan
      Abstract: By splitting idempotent morphisms in the total and base categories of fibrations we provide an explicit elementary description of the Cauchy completion of objects in the categories Fib( \(\mathbb {B}\) ) of fibrations with a fixed base category \(\mathbb {B}\) and Fib of fibrations with any base category. Two universal constructions are at issue, corresponding to two fibered reflections involving the fibration of fibrations \(\mathbf{Fib}\rightarrow \mathbf{Cat}\) .
      PubDate: 2018-02-06
      DOI: 10.1007/s00153-018-0616-5
  • Stationary sets added when forcing squares
    • Authors: Maxwell Levine
      Abstract: Current research in set theory raises the possibility that \(\square _{\kappa ,<\lambda }\) can be made compatible with some stationary reflection, depending on the parameter \(\lambda \) . The purpose of this paper is to demonstrate the difficulty in such results. We prove that the poset \({\mathbb {S}}(\kappa ,<\lambda )\) , which adds a \(\square _{\kappa ,<\lambda }\) -sequence by initial segments, will also add non-reflecting stationary sets concentrating in any given cofinality below \(\kappa \) . We also investigate the CMB poset, which adds \(\square _\kappa ^*\) in a slightly different way. We prove that the CMB poset also adds non-reflecting stationary sets, but not necessarily concentrating in any cofinality.
      PubDate: 2018-02-02
      DOI: 10.1007/s00153-018-0613-8
  • Hanf number for Scott sentences of computable structures
    • Authors: S. S. Goncharov; J. F. Knight; I. Souldatos
      Abstract: The Hanf number for a set S of sentences in \(\mathcal {L}_{\omega _1,\omega }\) (or some other logic) is the least infinite cardinal \(\kappa \) such that for all \(\varphi \in S\) , if \(\varphi \) has models in all infinite cardinalities less than \(\kappa \) , then it has models of all infinite cardinalities. Friedman asked what is the Hanf number for Scott sentences of computable structures. We show that the value is \(\beth _{\omega _1^{CK}}\) . The same argument proves that \(\beth _{\omega _1^{CK}}\) is the Hanf number for Scott sentences of hyperarithmetical structures.
      PubDate: 2018-02-01
      DOI: 10.1007/s00153-018-0615-6
  • Generic variations and NTP $$_1$$ 1
    • Authors: Jan Dobrowolski
      Abstract: We prove a preservation theorem for NTP \(_1\) in the context of the generic variations construction. We also prove that NTP \(_1\) is preserved under adding to a geometric theory a generic predicate.
      PubDate: 2018-01-27
      DOI: 10.1007/s00153-018-0609-4
  • Consistency of the intensional level of the Minimalist Foundation with
           Church’s thesis and axiom of choice
    • Authors: Hajime Ishihara; Maria Emilia Maietti; Samuele Maschio; Thomas Streicher
      Abstract: Consistency with the formal Church’s thesis, for short CT, and the axiom of choice, for short AC, was one of the requirements asked to be satisfied by the intensional level of a two-level foundation for constructive mathematics as proposed by Maietti and Sambin (in Crosilla, Schuster (eds) From sets and types to topology and analysis: practicable foundations for constructive mathematics, Oxford University Press, Oxford, 2005). Here we show that this is the case for the intensional level of the two-level Minimalist Foundation, for short MF, completed in 2009 by the second author. The intensional level of MF consists of an intensional type theory à la Martin-Löf, called mTT. The consistency of mTT with CT and AC is obtained by showing the consistency with the formal Church’s thesis of a fragment of intensional Martin-Löf’s type theory, called \(\mathbf{MLtt}_1\) , where mTT can be easily interpreted. Then to show the consistency of \(\mathbf{MLtt}_1\) with CT we interpret it within Feferman’s predicative theory of non-iterative fixpoints \(\widehat{ID_1}\) by extending the well known Kleene’s realizability semantics of intuitionistic arithmetics so that CT is trivially validated. More in detail the fragment \(\mathbf{MLtt}_1\) we interpret consists of first order intensional Martin-Löf’s type theory with one universe and with explicit substitution rules in place of usual equality rules preserving type constructors (hence without the so called \(\xi \) -rule which is not valid in our realizability semantics). A key difficulty encountered in our interpretation was to use the right interpretation of lambda abstraction in the applicative structure of natural numbers in order to model all the equality rules of \(\mathbf{MLtt}_1\) correctly. In particular the universe of \(\mathbf{MLtt}_1\) is modelled by means of \(\widehat{ID_1}\) -fixpoints following a technique due first to Aczel and used by Feferman and Beeson.
      PubDate: 2018-01-27
      DOI: 10.1007/s00153-018-0612-9
  • Closure properties of parametric subcompleteness
    • Authors: Gunter Fuchs
      Abstract: For an ordinal \(\varepsilon \) , I introduce a variant of the notion of subcompleteness of a forcing poset, which I call \(\varepsilon \) -subcompleteness, and show that this class of forcings enjoys some closure properties that the original class of subcomplete forcings does not seem to have: factors of \(\varepsilon \) -subcomplete forcings are \(\varepsilon \) -subcomplete, and if \(\mathbb {P}\) and \(\mathbb {Q}\) are forcing-equivalent notions, then \(\mathbb {P}\) is \(\varepsilon \) -subcomplete iff \(\mathbb {Q}\) is. I formulate a Two Step Theorem for \(\varepsilon \) -subcompleteness and prove an RCS iteration theorem for \(\varepsilon \) -subcompleteness which is slightly less restrictive than the original one, in that its formulation is more careful about the amount of collapsing necessary. Finally, I show that an adequate degree of \(\varepsilon \) -subcompleteness follows from the \(\kappa \) -distributivity of a forcing, for \(\kappa >\omega _1\) .
      PubDate: 2018-01-17
      DOI: 10.1007/s00153-018-0611-x
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