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Nonconstructivizable formal arithmetic structures
A. A. Tverskoi
Abstract:
Nonconstructivizability of a number of formal arithmetric structures is established in nonstandard models of formal Peano arithmetric ($PA$). Also considered is a formal structure whose constructivizability in a countable nonstandard model of $PA$ depends on the choice of the model. All concrete examples are built on formulas of class $\Delta_1(PA)$. Therefore the standard interpretations are recursive.
Bibliography: 12 titles.
Received: 07.01.1985
Citation:
A. A. Tverskoi, “Nonconstructivizable formal arithmetic structures”, Izv. Akad. Nauk SSSR Ser. Mat., 51:1 (1987), 111–130; Math. USSR-Izv., 30:1 (1988), 103–122
Linking options:
https://www.mathnet.ru/eng/im1265https://doi.org/10.1070/IM1988v030n01ABEH000995 https://www.mathnet.ru/eng/im/v51/i1/p111
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Abstract page: | 232 | Russian version PDF: | 83 | English version PDF: | 8 | References: | 48 | First page: | 1 |
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