We shall know: Hilbert's apology

Mathematical Intelligencer

Volumn 21, Issue 1, 1999, Pages 42-46

  Vinnikov, Victor ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033248799     PISSN: 03436993     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03024831     Document Type: Review

References (22)

1. [1] F. E. Browder (ed.), Mathematical developments arising from Hilbert problems, Proc. Symp. Pure Math., vol. 28, Amer. Math. Soc., Providence, 1976.
2. [2] M. Davis (ed.), The undecidable, Raven Press, Hewlett, New York, 1965.
3. [3] S. Feferman, Hilbert's program relativized: proof-theoretical and foundational reductions, J. Symb. Logic 53 (1988), 364-384.
4. [4] K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. f. Math. u. Phys. 38 (1931), 173-198, translated as On formally undecidable propositions of Principia Mathematica and related systems I, [2, pp. 5-38].
5. [5] H. B. Griffiths and P. J. Hilton, A comprehensive textbook of classical mathematics, Van Nostrand Reinhold, London, 1970.
6. [6] D. Hilbert, Mathematische Probleme, Göttinger Nachrichten (1900), 253-297 (reprinted in Archiv f. Math. u. Phys. 3. Reihe 1 (1901), 44-63 and 213-237; and in [8, Vol. 3, pp. 290-329]), translated as Mathematical Problems, Bull. Amer. Math. Soc. 8 (1902), 437-479 (reprinted in [1, pp. 1-34]).
7. [6] D. Hilbert, Mathematische Probleme, Göttinger Nachrichten (1900), 253-297 (reprinted in Archiv f. Math. u. Phys. 3. Reihe 1 (1901), 44-63 and 213-237; and in [8, Vol. 3, pp. 290-329]), translated as Mathematical Problems, Bull. Amer. Math. Soc. 8 (1902), 437-479 (reprinted in [1, pp. 1-34]).
8. [6] D. Hilbert, Mathematische Probleme, Göttinger Nachrichten (1900), 253-297 (reprinted in Archiv f. Math. u. Phys. 3. Reihe 1 (1901), 44-63 and 213-237; and in [8, Vol. 3, pp. 290-329]), translated as Mathematical Problems, Bull. Amer. Math. Soc. 8 (1902), 437-479 (reprinted in [1, pp. 1-34]).
9. [7] -, Naturerkennen und Logik, Naturwissenschaften (1930), 959-963 (reprinted in [8, Vol. 3, pp. 378-387]).
10. [8] -, Gesammelten Abhandlungen, Springer Verlag, Berlin-Heidelberg, 1935 (reprinted in 1970).
11. [9] -, Gedenkband, Springer-Verlag, Berlin-Heidelberg, 1971, edited by K. Reidemeister.
12. [10] S. C. Kleene, Introduction to metamathematics, Van Nostrand, New York 1952.
13. [11] -, Mathematical logic, Wiley, New York, 1967.
14. [12] C. Reid, Hilbert, Springer-Verlag, New York, 1970 (new edition as part of [13]).
15. [13] -, Hilbert-Courant, Springer-Verlag, New York, 1986.
16. [14] J. B. Rosser, Extensions of some theorems of Gödel and Church, J. Symb. Logic 1 (1936), 87-91 (reprinted in [2, pp. 231-235]).
17. [15] -, An informal exposition of proofs of Gödel's theorem and Church's theorem, J. Symb. Logic 4 (1939), 53-60 (reprinted in [2, pp. 223-230]).
18. [16] W. Sieg, Hilbert's program sixty years later, J. Symb. Logic 53 (1988), 338-348.
19. [17] S. Simpson, Partial realisations of Hilbert's programme, J. Symb. Logic 53 (1988), 349-363.
20. [18] H. Weyl, David Hilbert and his mathematical work, Bull. Amer. Math. Soc. 50 (1944), 612-654 (reprinted in [20, Vol. 4, pp. 130-172]).
21. [19] -, Mathematics and Logic. A brief survey serving as a preface to a review of "The Philosophy of Bertrand Russell", Amer. Math. Monthly 53 (1946), 2-13 (reprinted in [20, Vol. 4, pp. 268-279]).
22. [20] -, Gesammelten Abhandlungen, Springer-Verlag, Berlin-Heidelberg, 1968.