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Transactions of the American Mathematical Society

by S. C. Kleene

Trans. Amer. Math. Soc. 53 (1943), 41-73

DOI: https://doi.org/10.1090/S0002-9947-1943-0007371-8

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• Alonzo Church, An Unsolvable Problem of Elementary Number Theory, Amer. J. Math. 58 (1936), no. 2, 345–363. MR 1507159, DOI 10.2307/2371045
• Alonzo Church, The constructive second number class, Bull. Amer. Math. Soc. 44 (1938), no. 4, 224–232. MR 1563715, DOI 10.1090/S0002-9904-1938-06720-1
Alonzo Church and S. C. Kleene. 1. Formal definitions in the theory of ordinal numbers, Fund. Math. vol. 28 (1936) pp. 11-21.
• Alonzo Church and J. B. Rosser, Some properties of conversion, Trans. Amer. Math. Soc. 39 (1936), no. 3, 472–482. MR 1501858, DOI 10.1090/S0002-9947-1936-1501858-0
• Haskell B. Curry, Some aspects of the problem of mathematical rigor, Bull. Amer. Math. Soc. 47 (1941), 221–242. MR 4206, DOI 10.1090/S0002-9904-1941-07414-8
• Haskell B. Curry, The inconsistency of certain formal logics, J. Symbolic Logic 7 (1942), 115–117. MR 7366, DOI 10.2307/2269292
• Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38 (1931), no. 1, 173–198 (German). MR 1549910, DOI 10.1007/BF01700692
—On undecidable propositions of formal mathematical systems, notes of lectures at the Institute for Advanced Study, 1934. David Hilbert and Paul Bernays 1. Grundlagen der Mathematik, vol. 2, Berlin, Springer, 1939. Arend Heyting 1. Die formalen Regeln der intuitionistischen Mathematik, Preuss. Akad. Wiss. Sitzungsber, Phys.-math. Kl. 1930, pp. 57-71, 1. 158-169.
• S. C. Kleene, A Theory of Positive Integers in Formal Logic. Part I, Amer. J. Math. 57 (1935), no. 1, 153–173. MR 1507063, DOI 10.2307/2372027
• S. C. Kleene, General recursive functions of natural numbers, Math. Ann. 112 (1936), no. 1, 727–742. MR 1513071, DOI 10.1007/BF01565439
• S. C. Kleene, A note on recursive functions, Bull. Amer. Math. Soc. 42 (1936), no. 8, 544–546. MR 1563352, DOI 10.1090/S0002-9904-1936-06353-6
—On notation for ordinal numbers, J. Symbolic Logic vol. 3 (1938) pp. 150-155.
• S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals, Amer. J. Math. 66 (1944), 41–58. MR 9757, DOI 10.2307/2371894
—On the interpretation of intuitionislic number theory, Bull. Amer. Math. Soc. abstract 48-1-85.
• S. C. Kleene and J. B. Rosser, The inconsistency of certain formal logics, Ann. of Math. (2) 36 (1935), no. 3, 630–636. MR 1503240, DOI 10.2307/1968646
David Nelson 1. Recursive functions and intuitionislic number theory, under preparation. L. Post 1. Finite combinatory processes—formulation I, J. Symbolic Logic vol. 1 (1936) pp. 103-105.
• Willard Van Orman Quine, Mathematical Logic, W. W. Norton & Co. Inc., New York, 1940. MR 0002508
Barkley Rosser Extensions of some theorems of Gödel and Church, J. Symbolic Logic vol. 1 (1936) pp. 87-91. —Goödel theorems for non-constructive logics, ibid. vol. 2 (1937) pp. 129-137. Alfred Tarski Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica vol. 1 (1936) pp. 261-405. (Original in Polish, 1933.)
• Alfred Tarski, On undecidable statements in enlarged systems of logic and the concept of truth, J. Symbolic Logic 4 (1939), 105–112. MR 210, DOI 10.2307/2266444
A. M. Turing On computable numbers, with an application to the Entscheidungsproblem, Proc. London Math. Soc. (2) vol. 42 (1937) pp. 230-265. —Systems of logic based on ordinals, ibid. vol. 45 (1939) pp. 161-228.

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• © Copyright 1943 American Mathematical Society
• Journal: Trans. Amer. Math. Soc. 53 (1943), 41-73
• MSC: Primary 02.0X
• DOI: https://doi.org/10.1090/S0002-9947-1943-0007371-8
• MathSciNet review: 0007371

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