Abstract: One of the important characteristics of structures is degrees of semantic and syntactic rigidity, as well as indices of rigidity, showing how much the given structure differs from semantically rigid structures, i.e., structures with one-element automorphism groups, as well as syntactically rigid structures, i.e., structures covered by definable closure of the empty set. Issues of describing the degrees and indices of rigidity represents interest both in a general context and in relation to ordering theories and their models. In the given paper, we study possibilities for semantic and syntactic rigidity for ordered theories, i.e., the rigidity with respect to automorphism group and with respect to definable closure. We describe values for indices and degrees of semantic and syntactic rigidity for well-ordered sets, for discrete, dense, and mixed orders and for countable models of ℵ0-categorical weakly o-minimal theories. All possibilities for degrees of rigidity for countable linear orderings are described.

Cite: Kulpeshov B.S. , Sudoplatov S.V.
Variations of rigidity for ordered theories
Известия Иркутского государственного университета. Серия: Математика (Bulletin of Irkutsk State University. Series Mathematics). 2024. V.48. P.129-144. DOI: 10.26516/1997-7670.2024.48.129 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Jul 28, 2023
Accepted:	Feb 27, 2024
Published print:	Jun 7, 2024
Published online:	Jun 7, 2024

Identifiers:

Web of science:	WOS:001247802100009
Scopus:	2-s2.0-85195795728
Elibrary:	67350317
OpenAlex:	W4399438012

Citing:

DB	Citing
Scopus	2
Web of science	1

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