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Russian Mathematical Surveys, 2004, Volume 59, Issue 2, Pages 203–229
DOI: https://doi.org/10.1070/RM2004v059n02ABEH000715 (Mi rm715) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Kolmogorov and Gödel's approach to intuitionistic logic: current developments

S. N. Artemovab

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b City University of New York, Graduate Center
English version PDF (346 kB) Citations (26)
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DOI: https://doi.org/10.1070/RM2004v059n02ABEH000715
Abstract: Intuitionistic mathematics was created by Brouwer on the basis of constructive reasoning, where the existence of a proof was the criterion for truth. Kolmogorov and Gödel proposed interpreting intuitionistic logic on the basis of classical notions of a problem's solution and of provability. In 1933 Gödel made the first substantial step toward the building of such an interpretation. Despite much progress in the understanding of intuitionism, this task was not complete before the author's 1995 paper. This survey will cover the results of the past decade obtained within this framework.
Received: 04.11.2003
Russian version:
Uspekhi Matematicheskikh Nauk, 2004, Volume 59, Issue 2(356), Pages 9–36
DOI: https://doi.org/10.4213/rm715
Bibliographic databases:
Document Type: Article
UDC: 510.23, 510.24, 510.25, 510.642, 510.643, 510.648
MSC: Primary 03B34, 03F45, 03F55; Secondary 03B70, 03B20, 03B80
Language: English
Original paper language: Russian
Citation: S. N. Artemov, “Kolmogorov and Gödel's approach to intuitionistic logic: current developments”, Uspekhi Mat. Nauk, 59:2(356) (2004), 9–36; Russian Math. Surveys, 59:2 (2004), 203–229
Citation in format AMSBIB
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    • This publication is cited in the following 26 articles:
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    		Успехи математических наук Russian Mathematical Surveys
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