@article{b4157b8398fa4290a7598dfa87ef202d,
title = "Strong Degrees of Categoricity and Weak Density",
abstract = "It is well-known that every c.e. Turing degree is the degree of categoricity of a rigid structure. In this work we study the possibility of extension of this result to properly 2-c.e. degrees. We found a condition such that if a Δ02-degree is a degree of categoricity of a rigid structure and satisfies this condition then it must be c.e. Also we show that degrees of non-categoricity are dense in the c.e. degrees.",
keywords = "computable isomorphism, computably enumerable sets, degree of categoricity, rigid structure, Turing degrees, STABILITY, COMPUTABLE CATEGORICITY, SPECTRA, RECURSIVE STRUCTURES, AUTOSTABILITY",
author = "Bazhenov, {N. A.} and Kalimullin, {I. Sh} and Yamaleev, {M. M.}",
note = "Funding Information: The work was supported by the Russian Science Foundation, project no. 18-11-00028. Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = sep,
doi = "10.1134/S1995080220090048",
language = "English",
volume = "41",
pages = "1630--1639",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "Maik Nauka Publishing / Springer SBM",
number = "9",
}