Subjects -> MATHEMATICS (Total: 1028 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (729 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (729 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 2)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 1)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 38)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
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: 5)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 20)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 9)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 19)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 8)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 3)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 1)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 13)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 8)
American Journal of Operations Research     Open Access   (Followers: 7)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 9)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 14)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 4)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
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   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 3)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 2)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 19)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
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)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal  
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 17)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 1)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 2)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 3)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
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  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 2)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Advanced Mathematical Sciences     Open Access  
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: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 10)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 33)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
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  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)

        1 2 3 4 | Last

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Archive for Mathematical Logic
Journal Prestige (SJR): 0.909
Citation Impact (citeScore): 1
Number of Followers: 3  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0665 - ISSN (Online) 0933-5846
Published by Springer-Verlag Homepage  [2469 journals]
  • On the isomorphism problem for some classes of computable algebraic
           structures

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      Abstract: We establish that the isomorphism problem for the classes of computable nilpotent rings, distributive lattices, nilpotent groups, and nilpotent semigroups is \(\Sigma _{1}^{1}\) -complete, which is as complicated as possible. The method we use is based on uniform effective interpretations of computable binary relations into computable structures from the corresponding algebraic classes.
      PubDate: 2022-01-20
       
  • Reverse mathematics and semisimple rings

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      Abstract: This paper studies various equivalent characterizations of left semisimple rings from the standpoint of reverse mathematics. We first show that \(\mathrm ACA_{0}\) is equivalent to the statement that any left module over a left semisimple ring is semisimple over \(\mathrm RCA_{0}\) . We then study characterizations of left semisimple rings in terms of projective modules as well as injective modules, and obtain the following results: (1) \(\mathrm ACA_{0}\) is equivalent to the statement that any left module over a left semisimple ring is projective over \(\mathrm RCA_{0}\) ; (2) \(\mathrm ACA_{0}\) is equivalent to the statement that any left module over a left semisimple ring is injective over \(\mathrm RCA_{0}\) ; (3) \(\mathrm RCA_{0}\) proves the statement that if every cyclic left R-module is projective, then R is a left semisimple ring; (4) \(\mathrm ACA_{0}\) proves the statement that if every cyclic left R-module is injective, then R is a left semisimple ring.
      PubDate: 2022-01-17
       
  • Iterated multiplication in $$ VTC ^0$$ V T C 0

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      Abstract: We show that \( VTC ^0\) , the basic theory of bounded arithmetic corresponding to the complexity class  \(\mathrm {TC}^0\) , proves the \( IMUL \) axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the \(\mathrm {TC}^0\) iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, \( VTC ^0\) can also prove the integer division axiom, and (by our previous results) the \( RSUV \) -translation of induction and minimization for sharply bounded formulas. Similar consequences hold for the related theories \(\Delta ^b_1\text{- } CR \) and  \(C^0_2\) . As a side result, we also prove that there is a well-behaved \(\Delta _0\)  definition of modular powering in \(I\Delta _0+ WPHP (\Delta _0)\) .
      PubDate: 2022-01-04
       
  • A note on cut-elimination for classical propositional logic

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      Abstract: In Schwichtenberg (Studies in logic and the foundations of mathematics, vol 90, Elsevier, pp 867–895, 1977), Schwichtenberg fine-tuned Tait’s technique (Tait in The syntax and semantics of infinitary languages, Springer, pp 204–236, 1968) so as to provide a simplified version of Gentzen’s original cut-elimination procedure for first-order classical logic (Gallier in Logic for computer science: foundations of automatic theorem proving, Courier Dover Publications, London, 2015). In this note we show that, limited to the case of classical propositional logic, the Tait–Schwichtenberg algorithm allows for a further simplification. The procedure offered here is implemented on Kleene’s sequent system G4 (Kleene in Mathematical logic, Wiley, New York, 1967; Smullyan in First-order logic, Courier corporation, London, 1995). The specific formulation of the logical rules for G4 allows us to provide bounds on the height of cut-free proofs just in terms of the logical complexity of their end-sequent.
      PubDate: 2021-11-26
      DOI: 10.1007/s00153-021-00800-8
       
  • Remarks on weak amalgamation and large conjugacy classes in
           non-archimedean groups

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      Abstract: We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure M, Polish group G of permutations of M, and \(n \ge 1\) , G has a comeager n-diagonal conjugacy class iff the family of all n-tuples of G-extendable bijections between finitely generated substructures of M, has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fraïssé classes that are not homogenizable. Finally, we investigate 1- and 2-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces.
      PubDate: 2021-11-26
      DOI: 10.1007/s00153-021-00807-1
       
  • Between Hilbert and Gentzen: four-valued consequence systems and
           structural reasoning

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      Abstract: Structural reasoning is simply reasoning that is governed exclusively by structural rules. In this context a proof system can be said to be structural if all of its inference rules are structural. A logic is considered to be structuralizable if it can be equipped with a sound and complete structural proof system. This paper provides a general formulation of the problem of structuralizability of a given logic, giving specific consideration to a family of logics that are based on the Dunn–Belnap four-valued semantics. It is shown how sound and complete structural proof systems can be constructed for a spectrum of logics within different logical frameworks.
      PubDate: 2021-11-24
      DOI: 10.1007/s00153-021-00806-2
       
  • Many different uniformity numbers of Yorioka ideals

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      Abstract: Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals’ uniformity numbers can be pairwise different. In addition we show that, in the same forcing extension, for two other types of simple cardinal characteristics parametrised by reals (localisation and anti-localisation cardinals), for uncountably many parameters the corresponding cardinals are pairwise different.
      PubDate: 2021-11-24
      DOI: 10.1007/s00153-021-00809-z
       
  • A criterion for uniform finiteness in the imaginary sorts

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      Abstract: Let T be a theory. If T eliminates \(\exists ^\infty \) , it need not follow that \(T^{\mathrm {eq}}\) eliminates \(\exists ^\infty \) , as shown by the example of the p-adics. We give a criterion to determine whether \(T^{\mathrm {eq}}\) eliminates \(\exists ^\infty \) . Specifically, we show that \(T^{\mathrm {eq}}\) eliminates \(\exists ^\infty \) if and only if \(\exists ^\infty \) is eliminated on all interpretable sets of “unary imaginaries.” This criterion can be applied in cases where a full description of \(T^{\mathrm {eq}}\) is unknown. As an application, we show that \(T^{\mathrm {eq}}\) eliminates \(\exists ^\infty \) when T is a C-minimal expansion of ACVF.
      PubDate: 2021-11-23
      DOI: 10.1007/s00153-021-00803-5
       
  • Efficient elimination of Skolem functions in $$\text {LK}^\text {h}$$ LK h

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      Abstract: We present a sequent calculus with the Henkin constants in the place of the free variables. By disposing of the eigenvariable condition, we obtained a proof system with a strong locality property—the validity of each inference step depends only on its active formulas, not its context. Our major outcomes are: the cut elimination via a non-Gentzen-style algorithm without resorting to regularization and the elimination of Skolem functions with linear increase in the proof length for a subclass of derivations with cuts.
      PubDate: 2021-11-22
      DOI: 10.1007/s00153-021-00798-z
       
  • Monadic $$k\times j$$ k × j -rough Heyting algebras

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      Abstract: In this paper, we introduce the variety of algebras, which we call monadic \(k\times j\) -rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in \(3\times 2\) case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic \(k\times j\) -rough Heyting algebras. In order to this, an Esakia-style duality for these algebras is developed.
      PubDate: 2021-11-13
      DOI: 10.1007/s00153-021-00802-6
       
  • The covering number of the strong measure zero ideal can be above almost
           everything else

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      Abstract: We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal \({{\mathcal {S}}}{{\mathcal {N}}}\) . As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal invariant of the continuum. Even more, Sacks forcing can be used to force that \(\mathrm {non}({{\mathcal {S}}}{{\mathcal {N}}})<\mathrm {cov}({{\mathcal {S}}}{{\mathcal {N}}})<\mathrm {cof}({{\mathcal {S}}}{{\mathcal {N}}})\) , which is the first consistency result where more than two cardinal invariants associated with \({{\mathcal {S}}}{{\mathcal {N}}}\) are pairwise different. Another consequence is that \({{\mathcal {S}}}{{\mathcal {N}}}\subseteq s^0\) in ZFC where \(s^0\) denotes Marczewski’s ideal.
      PubDate: 2021-11-10
      DOI: 10.1007/s00153-021-00808-0
       
  • Reflection and not SCH with overlapping extenders

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      Abstract: We use the forcing with overlapping extenders (Gitik in Blowing up the power of a singular cardinal of uncountable cofinality, to appear in JSL) to give a direct construction of a model of \(\lnot \) SCH+Reflection.
      PubDate: 2021-11-09
      DOI: 10.1007/s00153-021-00805-3
       
  • Coanalytic ultrafilter bases

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      Abstract: We study the definability of ultrafilter bases on \(\omega \) in the sense of descriptive set theory. As a main result we show that there is no coanalytic base for a Ramsey ultrafilter, while in L we can construct \(\Pi ^1_1\) P-point and Q-point bases. We also show that the existence of a \({\varvec{\Delta }}^1_{n+1}\) ultrafilter is equivalent to that of a \({\varvec{\Pi }}^1_n\) ultrafilter base, for \(n \in \omega \) . Moreover we introduce a Borel version of the classical ultrafilter number and make some observations.
      PubDate: 2021-11-03
      DOI: 10.1007/s00153-021-00801-7
       
  • Short note: Least fixed points versus least closed points

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      Abstract: This short note is on the question whether the intersection of all fixed points of a positive arithmetic operator and the intersection of all its closed points can proved to be equivalent in a weak fragment of second order arithmetic.
      PubDate: 2021-11-01
      DOI: 10.1007/s00153-021-00761-y
       
  • Generalised stability of ultraproducts of finite residue rings

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      Abstract: We study ultraproducts of finite residue rings \(\prod \nolimits _{n\in {\mathbb {N}}} {\mathbb {Z}}/n{\mathbb {Z}}\diagup {\mathcal {U}} \) where \({\mathcal {U}}\) is a non-principal ultrafilter. We find sufficient conditions of the ultrafilter \({\mathcal {U}}\) to determine if the resulting ultraproduct \(\prod \nolimits _{n\in {\mathbb {N}}} {\mathbb {Z}}/n{\mathbb {Z}}\diagup {\mathcal {U}}\) has simple, NIP, \(\mathrm {NTP}_{2}\) but not simple nor NIP, or \(\mathrm {TP}_{2}\) theory, noting that all these four cases occur.
      PubDate: 2021-11-01
      DOI: 10.1007/s00153-021-00760-z
       
  • The theories of Baldwin–Shi hypergraphs and their atomic models

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      Abstract: We show that the quantifier elimination result for the Shelah-Spencer almost sure theories of sparse random graphs \(G(n,n^{-\alpha })\) given by Laskowski (Isr J Math 161:157–186, 2007) extends to their various analogues. The analogues will be obtained as theories of generic structures of certain classes of finite structures with a notion of strong substructure induced by rank functions and we will call the generics Baldwin–Shi hypergraphs. In the process we give a method of constructing extensions whose ‘relative rank’ is negative but arbitrarily small in context. We give a necessary and sufficient condition for the theory of a Baldwin–Shi hypergraph to have atomic models. We further show that for certain well behaved classes of theories of Baldwin–Shi hypergraphs, the existentially closed models and the atomic models correspond.
      PubDate: 2021-11-01
      DOI: 10.1007/s00153-021-00765-8
       
  • The abstract type of the real numbers

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      Abstract: In finite type arithmetic, the real numbers are represented by rapidly converging Cauchy sequences of rational numbers. Ulrich Kohlenbach introduced abstract types for certain structures such as metric spaces, normed spaces, Hilbert spaces, etc. With these types, the elements of the spaces are given directly, not through the mediation of a representation. However, these abstract spaces presuppose the real numbers. In this paper, we show how to set up an abstract type for the real numbers. The appropriateness of our construction works in tandem with the bounded functional interpretation.
      PubDate: 2021-11-01
      DOI: 10.1007/s00153-021-00772-9
       
  • Hereditary G-compactness

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      Abstract: We introduce the notion of hereditary G-compactness (with respect to interpretation). We provide a sufficient condition for a poset to not be hereditarily G-compact, which we use to show that any linear order is not hereditarily G-compact. Assuming that a long-standing conjecture about unstable NIP theories holds, this implies that an NIP theory is hereditarily G-compact if and only if it is stable (and by a result of Simon, this holds unconditionally for \(\aleph _0\) -categorical theories). We show that if G is definable over A in a hereditarily G-compact theory, then \(G^{00}_A=G^{000}_A\) . We also include a brief survey of sufficient conditions for G-compactness, with particular focus on those which can be used to prove or disprove hereditary G-compactness for some (classes of) theories.
      PubDate: 2021-11-01
      DOI: 10.1007/s00153-021-00763-w
       
  • Factorizing the $$\mathbf {Top}$$ Top – $$\mathbf {Loc}$$ Loc adjunction
           through positive topologies

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      Abstract: We characterize the category of Sambin’s positive topologies as the result of the Grothendieck construction applied to a doctrine over the category Loc of locales. We then construct an adjunction between the category of positive topologies and that of topological spaces Top, and show that the well-known adjunction between Top and Loc factors through the constructed adjunction.
      PubDate: 2021-11-01
      DOI: 10.1007/s00153-021-00768-5
       
  • The automorphism group and definability of the jump operator in the
           $$\omega $$ ω -enumeration degrees

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      Abstract: In the present paper, we show the first-order definability of the jump operator in the upper semi-lattice of the \(\omega \) -enumeration degrees. As a consequence, we derive the isomorphicity of the automorphism groups of the enumeration and the \(\omega \) -enumeration degrees.
      PubDate: 2021-11-01
      DOI: 10.1007/s00153-021-00766-7
       
 
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