Alonzo church:his life, his work and some of his miracles

History and Philosophy of Logic

Volumn 18, Issue 4, 1997, Pages 211-232

  Manzano, Maía ^a  

^a UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

[No Author keywords available]

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EID: 33746837887     PISSN: 01445340     EISSN: 14645149     Source Type: Journal    
DOI: 10.1080/01445349708837290     Document Type: Article

References (55)

1. Andrews, P.B., 1986. An Introduction to Mathematical Logic and Type Theory:To Truth through Proof Orlando, FL:Academic Press.
2. Barendregt, H.P., 1981. The Lambda Calculus, its Syntax and Semantics, Amsterdam:North-Holland Publishing Company.
3. Boolos, G.S., and Jeffrey, R.C., 1992. Computability and Logic, Cambridge:Cambridge University Press. revised and enlarged edition 1st edn 1974
4. Church, A., 1926. Alternatives to Zermelo’s assumption. Transaction of the American Mathematical Society, 29:178–208.
5. Church, A., 1928. On the law of excluded middle. Bulletin of the American Mathematical Society, 34:75–78.
6. Church, A., 1936a. A note on the Entscheidungsproblem. The Journal of Symbolic Logic, 1 (1):40–41.
7. Church, A., 1936b. An unsolvable problem of elementary number theory. American Journal of Mathematics, 58 (1)
8. Church, A., 1940. A formulation of the simple theory of types. The Journal of Symbolic Logic, 5 (1):56–68.
9. Church, A., 1941. The calculi of lambda conversion. Annals of Mathematics Studies, 6 (1)
10. Church, A., 1951. “ A formulation of the logic of sense and denotation ”. In Structure, Methods and Meaning:Essays in Honor of Henry M. Sheffer 3–24. New York Revised in Nous:1973 (7), 24-33; vol 1974 (8), 135-56; and 1993 (27), 141-57
11. Church, A., 1956. Introduction to Mathematical Logic, Vol. I, Princeton:Princeton University Press.
12. Church, A., 1976. Comparison of Russell’s resolution of the semantical antinomies with that of Tarski. The Journal of Symbolic Logic, 41 (4)
13. Church, A., and Kleene, S.C., 1936. Formal definitions in the theory of ordinal numbers. Fundamenta Mathematical, 28 (4):11–21.
14. Church, A., and Quine, W.V., 1952. Some theorems on definability and decidability. The Journal of Symbolic Logic, 17 (3)
15. Van Dalen, D., 1983. “ Algorithms and decision problems:a crash course in recursion theory ”. In A Handbook of Philosophical Logic, Edited by:Gabbay and Guenther. Vol. I, Dordrecht:Reidel.
16. Davis, M., 1965. The Undecidable, New York:Raven Press.
17. Davis, M., 1982. Why Gödel didn’t have Church’s thesis. Information and Control, 54:3–24.
18. Davis, M., 1988. “ Mathematical logic and the origins of modern computers ”. In The Universal Turing Machine:A Half-Century Survey, Edited by:Herken, R., Oxford:Oxford University Press.
19. Davis, M., 1995. American logic in the 1920s. Bulletin of Symbolic Logic, 1 (3)
20. Feferman, S., 1988. “ Turing in the Land of O(z) ”. In The Universal Turing Machine:A Half-Century Survey, Edited by:Herken, R., Oxford:Oxford University Press.
21. Gabbay, D., and Guenthner, F., 1983. Handbook of Philosophical Logic, Vol. I, Dordrecht:Reidel.
22. Gandy, R., 1988. “ The confluence of ideas in 1936 ”. In The Universal Turing Machine:A Half-Century Survey, Edited by:Herken, R., Oxford:Oxford University Press.
23. Heijenoort, J., 1967. From Frege to Gödel, Edited by:Heijenoort, J., Cambridge, MA:Harvard University Press.
24. Henkin, L., 1949. The completeness of the first-order functional calculus. Journal of Symbolic Logic, 14:159–166.
25. Henkin, L., 1950. Completeness in the theory of types. The Journal of Symbolic Logic, 15:81–91.
26. Henkin, L., 1953. Banishing the rule of substitution for functional variables. The American Mathematical Monthly, 67 (4)
27. Henkin, L., 1963. A theory of propositional types. Fundamenta Mathematicae, 52 (4):323–344.
28. Henkin, L., 1975. Identity as a logical primitive. Philosophia, 5 (4):31–45.
29. Henkin, L. The discovery of my completeness proofs, Dedicated to my teacher Alonzo Church, in his 91st year, Bulletin of Symbolic Logic 2 (2) (presented on 24 August 1993 at the XIX International Congress of History of Science, Zaragoza, Spain)
30. Herken, R., ed. 1988. The Universal Turing Machine:A Half-Century Survey, Oxford:Oxford University Press.
31. Hindley, R., and Seidin, J., 1986. Introduction to Combinators and λ-Calculus, Cambridge:Cambridge University Press.
32. Hubert, D., and Ackermann, W., 1928. Grundzüge der theoretischen Logik, Berlin:Springer-Verlag.
33. Hodges, A., 1992. Alan Turing:The Enigma, London:London:Burnett Books. Vintage
34. Horn, B.K.P., and Winston, P.H., 1981. LISP, Reading, MA:Addison-Wesley.
35. Kleene, S.C., 1935. A theory of positive integers in formal logic. American Journal of Mathematics, 57:153–173. 210-44
36. Kleene, S.C., 1936a. “ General recursive functions on natural numbers ”. In Mathematische Annalen, Vol. 112, 727–742. New York:Raven Press. reprinted in M. Davis The Undecidable
37. Kleene, S.C., 1936b. λ-definability and recursiveness. Duke Mathematical Journal, 2:340–353.
38. Kleene, S.C., 1936c. A note on recursive functions. Bulletin of the American Mathematical Society, 42:544–546.
39. Kleene, S.C., 1952. Introduction to Metamathematics, Amsterdam:North-Holland.
40. Kleene, S.C., 1967. Mathematical Logic, Chichester, New York:John Wiley & Sons.
41. Kleene, S.C., 1981. Origins of recursive function theory. Annals of History of Computing, 3:52–65.
42. Langford, C.H., 1928. Concerning logical principles. Bulletin of the American Mathematical Society, 28:16–40.
43. Löwenheim, L., 1915. “ On the possibilities in the calculus of relatives ”. In From Frege to Gödel, Edited by:Heijenoort, J., Cambridge, MA:Harvard University Press.
44. Manzano, M., 1996. Extensions of First-Order Logic, Cambridge:Cambridge University Press.
45. Odifreddi, P., 1989. Classical Recursion Theory, Amsterdam:North-Holland.
46. Post, E.L., 1927. Finite combinatory processes. Journal of Symbolic Logic, 2:103–105.
47. Shoenfield, J.R., 1967. Mathematical Logic, Reading, MA:Addison-Wesley.
48. Shoenfield, J.R., 1995. The mathematical work of S. C. Kleene. Bulletin of Symbolic Logic, 1 (1):9–43.
49. Smullyan, R., 1993. “ Recursion Theory for Metamathematics ”. In Oxford Logic Guides 22, Oxford:Oxford University Press.
50. Russell, B., 1908. “ Mathematical logic as based on the theory of types ”. In From Frege to Gödel, Edited by:Heijenoort, J., Cambridge, MA:Harvard University Press.
51. Russell, B., and Whitehead, A., 1910-1913. Principia Mathematica, Vol. 3, Cambridge:Cambridge University Press.
52. Tarski, A., Mostowski, A., and Robinson, R.M., 1953. Undecidable Theories, Amsterdam:North-Holland.
53. Turing, A., 1936. On computable numbers with an application to the ensheidungsproblem. Proceedings of the London Mathematical Society, 42:230–265.
54. Turing, A., 1937. Computability and λ-definability. Journal of Symbolic Logic, 2:153–63.
55. Wolper, S. 1983. ’A legend turns 80’, UCLA Monthly