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Fundamentalnaya i Prikladnaya Matematika, 1999, Volume 5, Issue 1, Pages 221–255
(Mi fpm375)
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This article is cited in 2 scientific papers (total in 2 papers)
On arithmetic complexity of the predicate logics of complete constructive arithmetic theories
V. E. Plisko M. V. Lomonosov Moscow State University
Abstract:
It is proved in this paper that the predicate logic of each complete constructive arithmetic theory $T$ having the existence property is $\Pi_1^T$-complete. In this connection the techniques of uniform partial truth definition for intuitionistic arithmetic theories is used. The main theorem is applied to the characterization of the predicate logic corresponding to certain variant of the notion of realizable predicate formula. Namely it is shown that the set of undisprovable predicate formulas is recursively isomorphic to the complement of the set $\emptyset^{(\omega +1)}$.
Received: 01.10.1997
Citation:
V. E. Plisko, “On arithmetic complexity of the predicate logics of complete constructive arithmetic theories”, Fundam. Prikl. Mat., 5:1 (1999), 221–255
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https://www.mathnet.ru/eng/fpm375 https://www.mathnet.ru/eng/fpm/v5/i1/p221
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Abstract page: | 276 | Full-text PDF : | 96 | First page: | 1 |
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