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Zapiski Nauchnykh Seminarov LOMI, 1974, Volume 40, Pages 110–118 (Mi znsl2686)  

On $E$-theorems

G. E. Mints
Abstract: There are [1] many methods to construct for every proof of a sentence $\exists x A$ in Heyting (intuitionistic) arithmetic $HA$ [2] a term $t_p$ such that $A[t_p]$ is true (in some sence). It turns out that majority of these methods are equivalent: correspondent terms $t_p$ are convertible into one and the same natural number. This is proved here for three methods: (I) complete cut-elimination in the infinite formulation of $HA$ [3]; (II) recursive realizability [2]; (III) partial cut-elimination along the lines of Gentsen's 2-nd consistency proof [5]. [6] or normalization [7], [8]. It is shown that the process of cut-elimination by method (I) leads only to computation of values of terms associated with a given proof by methods (II) and (III).
Bibliographic databases:
UDC: 51.01:164
Language: Russian
Citation: G. E. Mints, “On $E$-theorems”, Studies in constructive mathematics and mathematical logic. Part VI, Zap. Nauchn. Sem. LOMI, 40, "Nauka", Leningrad. Otdel., Leningrad, 1974, 110–118
Citation in format AMSBIB
\Bibitem{Min74}
\by G.~E.~Mints
\paper On $E$-theorems
\inbook Studies in constructive mathematics and mathematical logic. Part~VI
\serial Zap. Nauchn. Sem. LOMI
\yr 1974
\vol 40
\pages 110--118
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2686}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=398795}
\zmath{https://zbmath.org/?q=an:0368.02034}
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