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Mat. Tr., 2018, Volume 21, Number 2, Pages 3–60 (Mi mt337)  

A computable structure with non-standard computability

R. R. Avdeeva, V. G. Puzarenkoab

a Novosibirsk State University, Novosibirsk, 630090 Russia
b Sobolev Institute of Mathematics, Novosibirsk, 630090 Russia

Abstract: We find an example of a computable admissible set whose level of computability is higher than that of the standard model of Peano arithmetic. As a byproduct, we construct a $1$ model of an undecidable submodel complete theory.

Key words: admissible set, hyperadmissible set, hereditarily finite superstructure, recursively saturated model, computable model, decidable model, $\Sigma$-reducibility, $\Sigma$-definability.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00624_а
The work of the second author was partially supported by the Russian Foundation for Basic Research (project 18-01-00624).


DOI: https://doi.org/10.17377/mattrudy.2018.21.201

Full text: PDF file (491 kB)
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English version:
Siberian Advances in Mathematics, 2019, 29:2, 77–115

UDC: 510.5
Received: 13.09.2017

Citation: R. R. Avdeev, V. G. Puzarenko, “A computable structure with non-standard computability”, Mat. Tr., 21:2 (2018), 3–60; Siberian Adv. Math., 29:2 (2019), 77–115

Citation in format AMSBIB
\Bibitem{AvdPuz18}
\by R.~R.~Avdeev, V.~G.~Puzarenko
\paper A~computable structure with non-standard computability
\jour Mat. Tr.
\yr 2018
\vol 21
\issue 2
\pages 3--60
\mathnet{http://mi.mathnet.ru/mt337}
\crossref{https://doi.org/10.17377/mattrudy.2018.21.201}
\transl
\jour Siberian Adv. Math.
\yr 2019
\vol 29
\issue 2
\pages 77--115
\crossref{https://doi.org/10.3103/S1055134419020019}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85067695211}


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