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  1. Some theorems about the sentential calculi of Lewis and Heyting.J. C. C. McKinsey & Alfred Tarski - 1948 - Journal of Symbolic Logic 13 (1):1-15.
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  • Some Theorems About the Sentential Calculi of Lewis and Heyting.J. C. C. Mckinsey & Alfred Tarski - 1948 - Journal of Symbolic Logic 13 (3):171-172.
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  • A universal approach to self-referential paradoxes, incompleteness and fixed points.Noson S. Yanofsky - 2003 - Bulletin of Symbolic Logic 9 (3):362-386.
    Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.
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  • Boolean Algebras with Operators.Alfred Tarski - 1953 - Journal of Symbolic Logic 18 (1):70-71.
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  • A Proof of the Completeness Theorem of Godel.H. Rasiowa & R. Sikorski - 1952 - Journal of Symbolic Logic 17 (1):72-72.
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  • Algebraic Treatment of the Notion of Satisfiability.H. Rasiowa & R. Sikorski - 1955 - Journal of Symbolic Logic 20 (1):78-80.
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  • Algebraic Treatment of the Functional Calculi of Heyting and Lewis.H. Rasiowa - 1953 - Journal of Symbolic Logic 18 (1):72-73.
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  • An Application of Lattices to Logic.H. Rasiowa & R. Sikorski - 1970 - Journal of Symbolic Logic 35 (1):137-137.
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  • Algebraic Models of Axiomatic Theories.H. Rasiowa - 1968 - Journal of Symbolic Logic 33 (2):285-286.
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  • Conceptual completeness for first-order Intuitionistic logic: an application of categorical logic.Andrew M. Pitts - 1989 - Annals of Pure and Applied Logic 41 (1):33-81.
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  • On the structure of paradoxes.Du?ko Pavlovi? - 1992 - Archive for Mathematical Logic 31 (6):397-406.
    Paradox is a logical phenomenon. Usually, it is produced in type theory, on a type Ω of “truth values”. A formula Ψ (i.e., a term of type Ω) is presented, such that Ψ↔¬Ψ (with negation as a term¬∶Ω→Ω)-whereupon everything can be proved: In Sect. 1 we describe a general pattern which many constructions of the formula Ψ follow: for example, the well known arguments of Cantor, Russell, and Gödel. The structure uncovered behind these paradoxes is generalized in Sect. 2. This (...)
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  • The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
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  • On Closed Elements in Closure Algebras.J. C. C. Mckinsey & Alfred Tarski - 1946 - Annals of Mathematics, Ser. 2 47:122-162.
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  • Strong conceptual completeness for first-order logic.Michael Makkai - 1988 - Annals of Pure and Applied Logic 40 (2):167-215.
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  • A theorem on barr-exact categories, with an infinitary generalization.Michael Makkai - 1990 - Annals of Pure and Applied Logic 47 (3):225-268.
    Let C be a small Barr-exact category, Reg the category of all regular functors from C to the category of small sets. A form of M. Barr's full embedding theorem states that the evaluation functor e : C →[Reg, Set ] is full and faithful. We prove that the essential image of e consists of the functors that preserve all small products and filtered colimits. The concept of κ-Barr-exact category is introduced, for κ any infinite regular cardinal, and the natural (...)
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  • Functional Semantics of Algebraic Theories.F. William Lawvere - 1974 - Journal of Symbolic Logic 39 (2):340-341.
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  • Adjointness in Foundations.F. William Lawvere - 1969 - Dialectica 23 (3‐4):281-296.
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  • Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
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  • Cylindric Algebras.Leon Henkin & Alfred Tarski - 1967 - Journal of Symbolic Logic 32 (3):415-416.
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  • Three varieties of mathematical structuralism.Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):184-211.
    Three principal varieties of mathematical structuralism are compared: set-theoretic structuralism (‘STS’) using model theory, Shapiro's ante rem structuralism invoking sui generis universals (‘SGS’), and the author's modal-structuralism (‘MS’) invoking logical possibility. Several problems affecting STS are discussed concerning, e.g., multiplicity of universes. SGS overcomes these; but it faces further problems of its own, concerning, e.g., the very intelligibility of purely structural objects and relations. MS, in contrast, overcomes or avoids both sets of problems. Finally, it is argued that the modality (...)
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  • Does category theory provide a framework for mathematical structuralism?Geoffrey Hellman - 2003 - Philosophia Mathematica 11 (2):129-157.
    Category theory and topos theory have been seen as providing a structuralist framework for mathematics autonomous vis-a-vis set theory. It is argued here that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves. We propose a synthesis of Bell's many-topoi view and modal-structuralism. Surprisingly, a combination of mereology and plural quantification suffices to describe hypothetical large domains, recovering the Grothendieck method of universes. Both topos theory and set theory can be carried out (...)
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  • The Basic Concepts of Algebraic Logic.Paul R. Halmos - 1958 - Journal of Symbolic Logic 23 (2):223-223.
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  • Algebraic Logic.Paul Richard Halmos - 2014 - New York, NY, USA: Chelsea.
    2014 Reprint of 1962 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In "Algebraic Logic" Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra. This book addresses some of the problems of mathematical logic and the theory of polyadic Boolean algebras in particular. It is intended to be an efficient (...)
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  • Topologies for intermediate logics.Olivia Caramello - 2014 - Mathematical Logic Quarterly 60 (4-5):335-347.
    We investigate the problem of characterizing the classes of Grothendieck toposes whose internal logic satisfies a given assertion in the theory of Heyting algebras, and introduce natural analogues of the double negation and De Morgan topologies on an elementary topos for a wide class of intermediate logics.
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  • La logique Des topos.André Boileau & André Joyal - 1981 - Journal of Symbolic Logic 46 (1):6-16.
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  • Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.
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  • Lattice Theory.Garrett Birkhoff - 1950 - Journal of Symbolic Logic 15 (1):59-60.
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  • Structure in mathematics and logic: A categorical perspective.S. Awodey - 1996 - Philosophia Mathematica 4 (3):209-237.
    A precise notion of ‘mathematical structure’ other than that given by model theory may prove fruitful in the philosophy of mathematics. It is shown how the language and methods of category theory provide such a notion, having developed out of a structural approach in modern mathematical practice. As an example, it is then shown how the categorical notion of a topos provides a characterization of ‘logical structure’, and an alternative to the Pregean approach to logic which is continuous with the (...)
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  • Category theory for linear logicians.Richard Blute & Philip Scott - 2004 - In Thomas Ehrhard (ed.), Linear logic in computer science. New York: Cambridge University Press. pp. 316--3.
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  • The Pre-History of Mathematical Structuralism.Erich H. Reck & Georg Schiemer (eds.) - 2020 - Oxford: Oxford University Press.
    This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.
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  • Categories for the Working Mathematician.Saunders Maclane - 1971 - Springer.
    Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint (...)
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  • General Theory of Natural Equivalences.Saunders MacLane & Samuel Eilenberg - 1945 - Transactions of the American Mathematical Society:231-294.
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