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Sibirsk. Mat. Zh., 2018, Volume 59, Number 4, Pages 719–735 (Mi smj3006)  

Degrees of autostability relative to strong constructivizations of graphs

N. A. Bazhenovab, M. I. Marchukab

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

Abstract: We show that each computably enumerable Turing degree is a degree of autostability relative to strong constructivizations for a decidable directed graph. We construct a decidable undirected graph whose autostability spectrum relative to strong constructivizations is equal to the set of all $PA$-degrees.

Keywords: computable model, strongly constructivizable model, autostability, autostability relative to strong constructivizations, degree of autostability relative to strong constructivizations, autostability spectrum relative to strong constructivizations, $PA$-degree, computably enumerable degree, graph.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-60058 мол_а_дк
17-01-00247
N. A. Bazhenov was supported by the Russian Foundation for Basic Research (Grant 16-31-60058-mol_a_dk).
M. I. Marchuk was supported by the Russian Foundation for Basic Research (Grant 17-01-00247).


DOI: https://doi.org/10.17377/smzh.2018.59.401

Full text: PDF file (367 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:4, 565–577

Bibliographic databases:

UDC: 510.5
MSC: 35R30
Received: 01.11.2017

Citation: N. A. Bazhenov, M. I. Marchuk, “Degrees of autostability relative to strong constructivizations of graphs”, Sibirsk. Mat. Zh., 59:4 (2018), 719–735; Siberian Math. J., 59:4 (2018), 565–577

Citation in format AMSBIB
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\by N.~A.~Bazhenov, M.~I.~Marchuk
\paper Degrees of autostability relative to strong constructivizations of graphs
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 4
\pages 719--735
\mathnet{http://mi.mathnet.ru/smj3006}
\crossref{https://doi.org/10.17377/smzh.2018.59.401}
\elib{http://elibrary.ru/item.asp?id=35725387}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 4
\pages 565--577
\crossref{https://doi.org/10.1134/S0037446618040018}
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