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Publisher: Cambridge University Press   (Total: 367 journals)

 Bulletin of Symbolic Logic   [SJR: 1.405]   [H-I: 26]   [2 followers]  Follow        Subscription journal    ISSN (Print) 1079-8986 - ISSN (Online) 1943-5894    Published by Cambridge University Press  [367 journals]
• BSL volume 24 issue 1 Cover and Front matter
• PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.17
Issue No: Vol. 24, No. 1 (2018)

• BSL volume 24 issue 1 Cover and Back matter
• PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.18
Issue No: Vol. 24, No. 1 (2018)

• POLYMORPHISM AND THE OBSTINATE CIRCULARITY OF SECOND ORDER LOGIC: A
VICTIMS’ TALE
• Authors: PAOLO PISTONE
Pages: 1 - 52
Abstract: The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity (or impredicativity) of second and higher-order logic. However, the epistemological significance of such investigations has not received much attention in the contemporary foundational debate.We discuss Girard’s normalization proof for second order type theory or System F and compare it with two faulty consistency arguments: the one given by Frege for the logical system of the Grundgesetze (shown inconsistent by Russell’s paradox) and the one given by Martin-Löf for the intuitionistic type theory with a type of all types (shown inconsistent by Girard’s paradox).The comparison suggests that the question of the circularity of second order logic cannot be reduced to Russell’s and Poincaré’s 1906 “vicious circle” diagnosis. Rather, it reveals a bunch of mathematical and logical ideas hidden behind the hazardous idea of impredicative quantification, constituting a vast (and largely unexplored) domain for foundational research.
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2017.43
Issue No: Vol. 24, No. 1 (2018)

• A HIERARCHY OF COMPUTABLY ENUMERABLE DEGREES
• Authors: ROD DOWNEY; NOAM GREENBERG
Pages: 53 - 89
Abstract: We introduce a new hierarchy of computably enumerable degrees. This hierarchy is based on computable ordinal notations measuring complexity of approximation of ${\rm{\Delta }}_2^0$ functions. The hierarchy unifies and classifies the combinatorics of a number of diverse constructions in computability theory. It does so along the lines of the high degrees (Martin) and the array noncomputable degrees (Downey, Jockusch, and Stob). The hierarchy also gives a number of natural definability results in the c.e. degrees, including a definable antichain.
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2017.41
Issue No: Vol. 24, No. 1 (2018)

• A CONSTRUCTIVE EXAMINATION OF A RUSSELL-STYLE RAMIFIED TYPE THEORY
• Authors: ERIK PALMGREN
Pages: 90 - 106
Abstract: In this article we examine the natural interpretation of a ramified type hierarchy into Martin-Löf type theory with an infinite sequence of universes. It is shown that under this predicative interpretation some useful special cases of Russell’s reducibility axiom are valid, namely functional reducibility. This is sufficient to make the type hierarchy usable for development of constructive mathematical analysis in the style of Bishop. We present a ramified type theory suitable for this purpose. One may regard the results of this article as an alternative solution to the problem of the proliferation of levels of real numbers in Russell’s theory, which avoids impredicativity, but instead imposes constructive logic. The intuitionistic ramified type theory introduced here also suggests that there is a natural associated notion of predicative elementary topos.
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.4
Issue No: Vol. 24, No. 1 (2018)

• Flag+algebras.+Journal+of+Symbolic+Logic,+vol.+72+(2007),+no.+4,+pp.+1239–1282.&rft.title=Bulletin+of+Symbolic+Logic&rft.issn=1079-8986&rft.date=2018&rft.volume=24&rft.spage=107&rft.epage=108&rft.aulast=Cummings&rft.aufirst=James&rft.au=James+Cummings&rft_id=info:doi/10.1017/bsl.2018.11">Alexander Razborov, Flag algebras. Journal of Symbolic Logic, vol. 72
(2007), no. 4, pp. 1239–1282.
• Authors: James Cummings
Pages: 107 - 108
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.11
Issue No: Vol. 24, No. 1 (2018)

• 2016–17 WINTER MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC Hyatt
Regency Atlanta and Marriott Atlanta Marquis Atlanta, GA, USA January
6–7, 2017
• Pages: 109 - 118
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.9
Issue No: Vol. 24, No. 1 (2018)

• 2017 NORTH AMERICAN ANNUAL MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC
Boise State University Boise, ID, USA March 20–23, 2017
• Pages: 119 - 140
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.8
Issue No: Vol. 24, No. 1 (2018)

• Notices
• Pages: 141 - 146
PubDate: 2018-03-01T00:00:00.000Z
DOI: 10.1017/bsl.2018.16
Issue No: Vol. 24, No. 1 (2018)

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