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  1. added 2020-07-02
    Forcing and the Universe of Sets: Must We Lose Insight?Neil Barton - forthcoming - Journal of Philosophical Logic:1-38.
    A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...)
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  2. added 2020-06-26
    Rabin Michael O.. A Simple Method for Undecidability Proofs and Some Applications. Logic, Methodology and Philosophy of Science, Proceedings of the 1964 International Congress, Edited by Bar-Hillel Yehoshua, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam 1965, Pp. 38–68. [REVIEW]William Hanf - 1971 - Journal of Symbolic Logic 36 (1):150.
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  3. added 2020-06-26
    L. Novak Gál. A Note on Direct Products. The Journal of Symbolic Logic, Vol. 23 No. 1 , Pp. 1–6.G. Hasenjaeger - 1971 - Journal of Symbolic Logic 36 (3):541.
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  4. added 2020-06-26
    W. A. J. Luxemburg. A General Theory of Monads. Applications of Model Theory to Algebra, Analysis, and Probability, Edited by W. A. J. Luxemburg, Holt, Rinehart and Winston, New York, Chicago, San Francisco, Atlanta, Dallas, Montreal, Toronto, London, and Sidney, 1969, Pp. 18–86. [REVIEW]Louis Narens - 1971 - Journal of Symbolic Logic 36 (3):541-542.
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  5. added 2020-06-25
    Gerson B. Robison. An Introduction to Mathematical Logic. Prentice-Hall, Inc., Engle Wood Cliffs, N.J., 1969, Xii + 212 Pp. [REVIEW]William E. Gould - 1971 - Journal of Symbolic Logic 36 (4):679.
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  6. added 2020-06-25
    Thoralf A. Skolem. Abstract Set Theory. Notre Dame Mathematical Lectures, No. 8, University of Notre Dame, Notre Dame, Indiana, 1962, V + 70 Pp. [REVIEW]Perry Smith - 1971 - Journal of Symbolic Logic 36 (4):680.
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  7. added 2020-06-25
    Arthur Pap. Extensionality, Attributes, and Classes. Philosophical Studies , Vol. 9 , Pp. 42–46.Perry Smith - 1971 - Journal of Symbolic Logic 36 (4):675.
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  8. added 2020-06-25
    A. Heyting. After Thirty Years. Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, Edited by Ernest Nagel, Patrick Suppes, and Alfred Tarski, Stanford University Press, Stanford, California, 1962, Pp. 194–197. [REVIEW]O. Chateaubriand - 1971 - Journal of Symbolic Logic 36 (4):674.
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  9. added 2020-06-23
    Satoko Titani. An Algebraic Formulation of Cut-Elimination Theorem. Journal of the Mathematical Society of Japan, Vol. 17 , Pp. 72–83. [REVIEW]Moto-O. Takahashi - 1970 - Journal of Symbolic Logic 35 (1):145-146.
  10. added 2020-06-23
    M. H. Löb. Concatenation as Basis for a Complete System of Arithmetic. The Journal of Symbolic Logic, Vol. 18 , Pp. 1–6. - M. H. Löb. Formal Systems of Constructive Mathematics. The Journal of Symbolic Logic, Vol. 21 , Pp. 63–75. [REVIEW]Charles Parsons - 1970 - Journal of Symbolic Logic 35 (1):150-150.
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  11. added 2020-06-23
    Julia Robinson. The Undecidability of Exponential Diophantine Equations. Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, Edited by Ernest Nagel, Patrick Suppes, and Alfred Tarski, Stanford University Press, Stanford, Calif., 1962, Pp. 12–13. [REVIEW]Hartley Rogers - 1970 - Journal of Symbolic Logic 35 (1):152.
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  12. added 2020-06-23
    L. J. Heider. Prime Dual Ideals in Boolean Algebras. Canadian Journal of Mathematics, Vol. 11 , Pp. 397–408.Robert LaGrange - 1969 - Journal of Symbolic Logic 33 (4):624.
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  13. added 2020-06-23
    P. M. Cohn. Universal Algebra. Harper & Row, Publishers, New York, Evanston, and London, 1965, Xv + 333 Pp. [REVIEW]Abraham Robinson - 1969 - Journal of Symbolic Logic 34 (1):113-114.
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  14. added 2020-06-23
    Roger C. Lyndon. Metamathematics and Algebra: An Example. Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, Edited by Ernest Nagel, Patrick Suppes, and Alfred Tarski, Stanford University Press, Stanford1962, Pp. 143–150. [REVIEW]Arnold Oberschelp - 1969 - Journal of Symbolic Logic 34 (4):653.
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  15. added 2020-06-23
    J. R. Shoenfield. The Problem of Predicativity. Essays on the Foundations of Mathematics, Dedicated to A. A. Fraenkel on His Seventieth Anniversary, Edited by Y. Bar-Hillel, E. I. J. Poznanski, M. O. Rabin, and A. Robinson for The Hebrew University of Jerusalem, Magnes Press, Jerusalem1961, and North-Holland Publishing Company, Amsterdam 1962, Pp. 132–139. [REVIEW]George S. Boolos - 1969 - Journal of Symbolic Logic 34 (3):515.
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  16. added 2020-06-23
    G. Kreisel and J. L. Krivine. Elements of Mathematical Logic. . North-Holland Publishing Company, Amsterdam1967, Xi + 222 Pp. [REVIEW]C. C. Chang - 1969 - Journal of Symbolic Logic 34 (1):112.
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  17. added 2020-06-21
    Metrically Homogeneous Graphs of Diameter 3.Daniela A. Amato, Gregory Cherlin & H. Dugald Macpherson - forthcoming - Journal of Mathematical Logic:2050020.
    We classify countable metrically homogeneous graphs of diameter 3.
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  18. added 2020-06-21
    Gustav Hensel and Hilary Putnam. On the Notational Independence of Various Hierarchies of Degrees of Unsolvability. The Journal of Symbolic Logic, Vol. 30 , Pp. 69–86.Ylannis N. Moschovakis - 1967 - Journal of Symbolic Logic 32 (1):124-125.
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  19. added 2020-06-21
    John Myhill. Recursive Equivalence Types and Combinatorial Functions. Logic, Methodology and Philosophy of Science, Proceedings of the 1960 International Congress, Edited by Ernest Nagel, Patrick Suppes, and Alfred Tarski, Stanford University Press, Stanford, Calif., 1962, Pp. 46–55. [REVIEW]J. C. E. Dekker - 1966 - Journal of Symbolic Logic 31 (3):510-511.
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  20. added 2020-06-21
    K. I. Appel. Horn Sentences in Identity Theory. The Journal of Symbolic Logic, Vol. 24 No. 4 , Pp. 306–310.H. Jerome Keisler - 1966 - Journal of Symbolic Logic 31 (1):131-132.
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  21. added 2020-06-21
    A. H. Lightstone. The Axiomatic Method. An Introduction to Mathematical Logic.Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964, X + 246 Pp. [REVIEW]Peter Andrews - 1966 - Journal of Symbolic Logic 31 (1):106-108.
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  22. added 2020-06-21
    G. Kreisel, J. Shoenfield, and Hao Wang. Number Theoretic Concepts and Recursive Well-Orderings. Archiv Für Mathematische Logik Und Grundlagenforschung, Vol. 5 , Pp. 42–64. [REVIEW]Ann M. Singleterry - 1966 - Journal of Symbolic Logic 31 (3):511-512.
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  23. added 2020-06-21
    Hartley RogersJr., The Present Theory of Turing Machine Computability. Journal of the Society for Industrial and Applied Mathematics, Vol. 7 , Pp. 114–130. [REVIEW]C. E. M. Yates - 1966 - Journal of Symbolic Logic 31 (3):513-513.
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  24. added 2020-06-19
    Helena Rasiowa and Roman Sikorski. The Mathematics of Metamathematics. Monografie Matematyczne, Vol. 41. Państwowe Wydawnictwo Naukowe, Warsaw1963, 519 Pp. [REVIEW]Donald Monk - 1967 - Journal of Symbolic Logic 32 (2):274-275.
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  25. added 2020-06-19
    Georg Kreisel. Mathematical Logic. Lectures on Modern Mathematics, Vol. 3, Edited by T. L. Saaty, John Wiley & Sons, Inc., New York, London, and Sydney, 1965, Pp. 95–195. [REVIEW]R. E. Vesley - 1967 - Journal of Symbolic Logic 32 (3):419-420.
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  26. added 2020-06-17
    Erwin Engeler. A Reduction-Principle for Infinite Formulas. Mathematische Annalen, Vol. 151 , Pp. 296–301.Carol Karp - 1968 - Journal of Symbolic Logic 33 (1):123.
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  27. added 2020-06-17
    Patrick Suppes and Shirley Hill. First Course in Mathematical Logic. Blaisdell Publishing Company, New York, Toronto, and London, 1964, Ix + 274 Pp. [REVIEW]Ann M. Singleterry - 1967 - Journal of Symbolic Logic 32 (3):421-422.
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  28. added 2020-06-17
    Patrick Suppes. Mathematical Logic for the Schools. The Arithmetic Teacher, Vol. 9 , Pp. 396–399. - Patrick Suppes and Frederick Binford. Experimental Teaching of Mathematical Logic in the Elementary School. The Arithmetic Teacher, Vol. 12 , Pp. 187–195. [REVIEW]Ann M. Singleterry - 1967 - Journal of Symbolic Logic 32 (3):422.
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  29. added 2020-06-17
    Hao Wang. Certain Predicates Defined by Induction Schemata. The Journal of Symbolic Logic, Vol. 18 , Pp. 49–59. Reprinted in A Survey of Mathematical Logic, by Hao Wang, Studies in Logic and the Foundations of Mathematics, Science Press, Peking, and North-Holland Publishing Company, Amsterdam, 1963, Pp. 535–545. [REVIEW]Steven Orey - 1965 - Journal of Symbolic Logic 30 (1):99-100.
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  30. added 2020-06-17
    Raymond M. Smullyan. Theory of Formal Systems. Annals of Mathematics Studies, No. 47. Princeton University Press, Princeton1961, Xi + 142 Pp. - Raymond M. Smullyan. Theory of Formal Systems. Revised Edition. Annals of Mathematics Studies, No. 47. Princeton University Press, Princeton1961, Xi + 147 Pp. [REVIEW]Marian Boykan Pour-El - 1965 - Journal of Symbolic Logic 30 (1):88-90.
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  31. added 2020-06-17
    Leon Henkin, W. Norman Smith, Verne J. Varineau, Michael J. Walsh. Retracing Elementary Mathematics. The Macmillan Company, New York1962, Xviii + 418 Pp. [REVIEW]Theodore Hailperin - 1964 - Journal of Symbolic Logic 29 (4):209.
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  32. added 2020-06-16
    Willard Van Orman Quine. Mathematical Logic. Revised Edition. Harper Torchbooks. The Science Library. Harper & Row, New York and Evanston1962, Xii + 346 Pp. [REVIEW]Frederic B. Fitch - 1964 - Journal of Symbolic Logic 29 (2):92.
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  33. added 2020-06-16
    R. O. Gandy. On a Problem of Kleene's. Bulletin of the American Mathematical Society, Vol. 66 , Pp. 501–502.Wayne Richter - 1964 - Journal of Symbolic Logic 29 (2):104.
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  34. added 2020-06-16
    Abraham Robinson. Introduction to Model Theory and to the Metamathematics of Algebra. Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Company, Amsterdam1963, IX + 284 Pp. [REVIEW]Carol R. Karp - 1964 - Journal of Symbolic Logic 29 (1):56.
  35. added 2020-06-16
    Norwood Russell Hanson. A Note on the Gödel Theorem. Notre Dame Journal of Formal Logic, Vol. 2 , P. 228.Alonzo Church - 1963 - Journal of Symbolic Logic 28 (4):295.
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  36. added 2020-06-10
    On Representations of Intended Structures in Foundational Theories.Neil Barton, Moritz Müller & Mihai Prunescu - manuscript
    Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...)
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  37. added 2020-06-01
    Double Negation Semantics for Generalisations of Heyting Algebras.Rob Arthan & Paulo Oliva - forthcoming - Studia Logica:1-25.
    This paper presents an algebraic framework for investigating proposed translations of classical logic into intuitionistic logic, such as the four negative translations introduced by Kolmogorov, Gödel, Gentzen and Glivenko. We view these as variant semantics and present a semantic formulation of Troelstra’s syntactic criteria for a satisfactory negative translation. We consider how each of the above-mentioned translation schemes behaves on two generalisations of Heyting algebras: bounded pocrims and bounded hoops. When a translation fails for a particular class of algebras, we (...)
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  38. added 2020-06-01
    Satisfiability is False Intuitionistically: A Question From Dana Scott.Charles McCarty - forthcoming - Studia Logica:1-11.
    Satisfiability or Sat\ is the metatheoretic statementEvery formally intuitionistically consistent set of first-order sentences has a model.The models in question are the Tarskian relational structures familiar from standard first-order model theory, but here treated within intuitionistic metamathematics. We prove that both IZF, intuitionistic Zermelo–Fraenkel set theory, and HAS, second-order Heyting arithmetic, prove Sat\ to be false outright. Following the lead of Carter :75–95, 2008), we then generalize this result to some provably intermediate first-order logics, including the Rose logic. These metatheorems (...)
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  39. added 2020-06-01
    Notice of Retraction: Pseudofinite Difference Field.Tingxiang Zou - forthcoming - Journal of Mathematical Logic:1993001.
    Journal of Mathematical Logic, Ahead of Print.
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  40. added 2020-06-01
    The FAN Principle and Weak König's Lemma in Herbrandized Second-Order Arithmetic.Fernando Ferreira - 2020 - Annals of Pure and Applied Logic 171 (9):102843.
    We introduce a herbrandized functional interpretation of a first-order semi-intuitionistic extension of Heyting Arithmetic and study its main properties. We then extend the interpretation to a certain system of second-order arithmetic which includes a (classically false) formulation of the FAN principle and weak König's lemma. It is shown that any first-order formula provable in this system is classically true. It is perhaps worthy of note that, in our interpretation, second-order variables are interpreted by finite sets of natural numbers.
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  41. added 2020-06-01
    Structure and Representation of Semimodules Over Inclines.Ruiqi Bai & Yichuan Yang - 2020 - Annals of Pure and Applied Logic 171 (10):102844.
    An incline S is a commutative semiring where r+1=1 for any r \in S . We note that the ideal lattice of an S-semimodule is naturally an S-semimodule and so is its congruence lattice when S is transitive. We prove that the categories of complete S-semimodules, together with dual functor, internal hom and tensor product, is a ⋆-autonomous category. We define the locally and globally maximal congruences which are related to Birkhoff subdirect product decomposition. We show that the categories of (...)
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  42. added 2020-06-01
    The Balanced Pseudocomplemented Ockham Algebras with the Strong Endomorphism Kernel Property.Jie Fang - 2019 - Studia Logica 107 (6):1261-1277.
    An endomorphism on an algebra \ is said to be strong if it is compatible with every congruence on \; and \ is said to have the strong endomorphism kernel property if every congruence on \, other than the universal congruence, is the kernel of a strong endomorphism on \. Here we characterise the structure of Ockham algebras with balanced pseudocomplementation those that have this property via Priestley duality.
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  43. added 2020-06-01
    Varieties of BL-Algebras III: Splitting Algebras.Paolo Aglianó - 2019 - Studia Logica 107 (6):1235-1259.
    In this paper we investigate splitting algebras in varieties of logics, with special consideration for varieties of BL-algebras and similar structures. In the case of the variety of all BL-algebras a complete characterization of the splitting algebras is obtained.
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  44. added 2020-06-01
    An Examination of Counterexamples in Proofs and Refutations.Samet Bağçe & Can Başkent - 2009 - Philosophia Scientae 13:3-20.
  45. added 2020-05-26
    Natural Formalization: Deriving the Cantor-Bernstein Theorem in Zf.Wilfried Sieg & Patrick Walsh - forthcoming - Review of Symbolic Logic:1-44.
    Natural Formalization proposes a concrete way of expanding proof theory from the meta-mathematical investigation of formal theories to an examination of “the concept of the specifically mathematical proof.” Formal proofs play a role for this examination in as much as they reflect the essential structure and systematic construction of mathematical proofs. We emphasize three crucial features of our formal inference mechanism: (1) the underlying logical calculus is built for reasoning with gaps and for providing strategic directions, (2) the mathematical frame (...)
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  46. added 2020-05-26
    Forms of Structuralism: Bourbaki and the Philosophers.Jean-Pierre Marquis - forthcoming - In Alberto Peruzzi & Silvano Zipoli Caiani (eds.), Structures Meres, Semantics, Mathematics, and Cognitive Science. New York, NY, USA:
    In this paper, we argue that, contrary to the view held by most philosophers of mathematics, Bourbaki’s technical conception of mathematical structuralism is relevant to philosophy of mathematics. In fact, we believe that Bourbaki has captured the core of any mathematical structuralism.
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  47. added 2020-05-26
    Remarks on Generic Stability in Independent Theories.Gabriel Conant & Kyle Gannon - 2020 - Annals of Pure and Applied Logic 171 (2):102736.
    In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of “generic stability” in arbitrary theories. Among other things, we show that the standard definition of generic stability for types coincides with the notion of a frequency interpretation measure. We also give combinatorial examples of types in NSOP theories that are finitely approximated but not generically stable, as well as ϕ-types in simple theories that are definable and finitely satisfiable in a small (...)
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  48. added 2020-05-26
    Functional Representation of Finitely Generated Free Algebras in Subvarieties of BL-Algebras.Manuela Busaniche, José Luis Castiglioni & Noemí Lubomirsky - 2020 - Annals of Pure and Applied Logic 171 (2):102757.
    Consider any subvariety of BL-algebras generated by a single BL-chain which is the ordinal sum of the standard MV-algebra on [0, 1] and a basic hoop H. We present a geometrical characterization of elements in the finitely generated free algebra of each of these subvarieties. In this characterization there is a clear insight of the role of the regular and dense elements of the generating chain. As an application, we analyze maximal and prime filters in the free algebra.
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  49. added 2020-05-26
    Feasibly Constructive Proofs of Succinct Weak Circuit Lower Bounds.Moritz Müller & Ján Pich - 2020 - Annals of Pure and Applied Logic 171 (2):102735.
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  50. added 2020-05-25
    Defining Integer Valued Functions in Rings of Continuous Definable Functions Over a Topological Field.Luck Darnière & Marcus Tressl - forthcoming - Journal of Mathematical Logic.
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