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Proof theory in the USSR 1925–1969

Published online by Cambridge University Press:  12 March 2014

Grigori Mints
Grigori Mints*
Affiliation:
Institute of Cybernetics, Academy of Sciences of the Estonian SSR, Tallinn 200108, USSR
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Abstract

We present a survey of proof theory in the USSR beginning with the paper by Kolmogorov [1925] and ending (mostly) in 1969; the last two sections deal with work done by A. A. Markov and N. A. Shanin in the early seventies, providing a kind of effective interpretation of negative arithmetic formulas. The material is arranged in chronological order and subdivided according to topics of investigation. The exposition is more detailed when the work is little known in the West or the original presentation can be improved using notions or results which appeared later. This includes such topics as Novikov's cut-elimination method (regular formulas) and Maslov's inverse method for the predicate logic.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 2 , June 1991 , pp. 385 - 424
Copyright
Copyright © Association for Symbolic Logic 1991

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References

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