Abstract:
We prove that a computable ordinal αα is autostable relative to strong constructivizations if and only if α<ωω+1α<ωω+1. We calculate, in a precise way, the complexity of the index set for linear orderings that are autostable relative to strong constructivizations.
Keywords:
computable model, strongly constructivizable model, autostability, autostability relative to strong constructivizations, linear ordering, computable ordinal, index set.
Citation:
S. S. Goncharov, N. A. Bazhenov, M. I. Marchuk, “The index set of linear orderings that are autostable relative to strong constructivizations”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:3 (2015), 51–60; J. Math. Sci., 221:6 (2017), 840–848
\Bibitem{GonBazMar15}
\by S.~S.~Goncharov, N.~A.~Bazhenov, M.~I.~Marchuk
\paper The index set of linear orderings that are autostable relative to strong constructivizations
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2015
\vol 15
\issue 3
\pages 51--60
\mathnet{http://mi.mathnet.ru/vngu375}
\crossref{https://doi.org/10.17377/PAM.2015.15.304}
\transl
\jour J. Math. Sci.
\yr 2017
\vol 221
\issue 6
\pages 840--848
\crossref{https://doi.org/10.1007/s10958-017-3272-0}
Linking options:
https://www.mathnet.ru/eng/vngu375
https://www.mathnet.ru/eng/vngu/v15/i3/p51
This publication is cited in the following 5 articles:
N. A. Bazhenov, M. I. Marchuk, “O spektrakh razreshimoi kategorichnosti dlya pochti prostykh modelei”, Algebra i logika, 62:4 (2023), 441–457
N. A. Bazhenov, “Categoricity spectra of computable structures”, J. Math. Sci. (N. Y.), 256:1 (2021), 34–50
Nikolay Bazhenov, Margarita Marchuk, Lecture Notes in Computer Science, 10936, Sailing Routes in the World of Computation, 2018, 40
S. S. Goncharov, N. A. Bazhenov, M. I. Marchuk, “The index set of the groups autostable relative to strong constructivizations”, Siberian Math. J., 58:1 (2017), 72–77
M. I. Marchuk, “Index set of structures with two equivalence relations that are autostable relative to strong constructivizations”, Algebra and Logic, 55:4 (2016), 306–314
Citation in format AMSBIB
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