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Book Review

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Book Information:

Author: Dennis E. Hesseling
Title: Gnomes in the fog: The reception of Brouwer's intuitionism in the 1920s
Additional book information: Science Networks -- Historical Studies, vol.~28, Birkhäuser, Basel, 2003, xxviii + 447 pp., ISBN 3-7643-6536-6, CHF 168.00 (EUR 115.56)

References [Enhancements On Off] (What's this?)

  • [Bi] Errett Bishop, ``Foundations of Constructive Analysis'', McGraw-Hill, New York, 1967. MR 36:4930
  • [Du] Michael Dummett, ``The philosophical basis of intuitionistic logic'', Proceedings of the Logic Colloquium, Bristol, July 1973, ed. H. E. Rose and J. C. Shepherdson, pp. 5-40, North-Holland, Amsterdam, 1975. Reprinted in Paul Benacerraf and Hilary Putnam, eds., ``Philosophy of Mathematics: Selected Readings'', 2nd ed., Cambridge University Press, Cambridge, 1983. MR 55:12449
  • [Gö] Kurt Gödel, ``Zur intuitionistischen Arithmetik und Zahlentheorie'', Ergebnisse eines mathematischen Kolloquiums, Heft 4, pp. 34-38, 1933.
  • [Kl45] S. C. Kleene, ``On the interpretation of intuitionistic number theory'', Jour. Symbolic Logic, vol. 10, pp. 109-124, 1945. MR 7:406a
  • [Kl52] S. C. Kleene, ``Introduction to Metamathematics'', North-Holland, Amsterdam, 1971. First published 1952. MR 14:525m
  • [M-L] Per Martin-Löf, ``Intuitionistic Type Theory'', Bibliopolis, Naples, 1984. MR 86j:03005
  • [DNe] David Nelson, ``Recursive functions and intuitionistic number theory'', Trans. Amer. Math. Soc., vol. 61, pp. 307-368, 1947. MR 10:3a
  • [ENe] Edward Nelson, ``Understanding Intuitionism'', presented at Rencontre du Reseau Georges Reeb, March 24-28, 1997, http://www.math.princeton.edu/ $\scriptstyle\sim$nelson/papers/int.pdf
  • [NoPeSm] Bengt Nordström, Kent Petersson, Jan M. Smith, ``Programming in Martin-Löf's Type Theory: An Introduction'', The International Series of Monographs on Computer Science, 7, Clarendon Press, Oxford, 1990. MR 94g:68020

Review Information:

Reviewer: Edward Nelson
Affiliation: Princeton University
Email: nelson@math.princeton.edu
Journal: Bull. Amer. Math. Soc. 41 (2004), 545-549
MSC (2000): Primary 01A60, 03-03, 03F55, 03B20
Published electronically: June 17, 2004
Review copyright: © Copyright 2004 American Mathematical Society
American Mathematical Society