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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 1, Pages 111–130 (Mi izv1265)  

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.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 30:1, 103–122

Bibliographic databases:

UDC: 517.12
MSC: Primary 03H15; Secondary 03C62
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

Citation in format AMSBIB
\Bibitem{Tve87}
\by A.~A.~Tverskoi
\paper Nonconstructivizable formal arithmetic structures
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 1
\pages 111--130
\mathnet{http://mi.mathnet.ru/izv1265}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=887603}
\zmath{https://zbmath.org/?q=an:0659.03037|0646.03053}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 30
\issue 1
\pages 103--122
\crossref{https://doi.org/10.1070/IM1988v030n01ABEH000995}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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