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Russian Math. Surveys 59:2 203--229 c #2004 RAS(DoM) and LMS

Summary: Russian Math. Surveys 59:2 203--229 c
#2004 RAS(DoM) and LMS
Uspekhi Mat. Nauk 59:2 9--36 DOI 10.1070/RM2004v059n02ABEH000715
Kolmogorov and G˜odel's approach to
intuitionistic logic: current developments
S. N. Artemov
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 G˜odel proposed interpreting intuitionistic logic on the basis of
classical notions of a problem's solution and of provability. In 1933 G˜odel 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 [17]. This survey will cover the results of the past decade
obtained within this framework.
§1. Introduction 203
§2. The Kolmogorov--G˜odel approach 206
§3. The Logic of Proofs 209
§4. Two models of provabiltiy 213
§5. Further developments 215


Source: Artemov, Sergei N. - Faculty of Mechanics and Mathematics, Moscow State University


Collections: Computer Technologies and Information Sciences