Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega | Sciact - Система учета научной деятельности ИМ СО РАН

Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega Научная публикация

Журнал

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Вых. Данные

Год: 2026, Том: 64, Номер: 6, Страницы: 397-401 Страниц : 5 DOI: 10.1007/s10469-026-09842-4

Ключевые слова

decidable structure, decidable categoricity, index set, computable ordinal, finitely axiomatizable class

Авторы

Bazhenov N.A. ^1,3 , Zubkov M.V. ² , Marchuk M.I. ³

Организации

1	Novosibirsk State University, Novosibirsk, Russia
2	Kazan Federal University, Kazan and Innopolis University, Innopolis, Russia
3	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Информация о финансировании (2)

1	Министерство науки и высшего образования РФ	075-15-2025-349
2	Российский научный фонд	25-21-00228

A strongly constructivizable model S is decidably categorical if for any decidable copies A and B of S, there exists a computable isomorphism from A onto B. The paper investigates the complexity of families of decidably categorical models belonging to familiar finitely axiomatizable classes. For a non-zero natural number n, the index set of decidably categorical linear orders elementarily equivalent to the ordinal ωn is an m-complete Σ0 2n+2-set. The index set of decidably categorical structures which are elementarily equivalent to ωn, enriched by the successor relation, is an m-complete Σ0 2n+1-set.

Bazhenov N.A. , Zubkov M.V. , Marchuk M.I.
Index Sets of Decidably Categorical Models that are Elementarily Equivalent to the Powers of Omega
Algebra and Logic. 2026. V.64. N6. P.397-401. DOI: 10.1007/s10469-026-09842-4 WOS Scopus OpenAlex

Поступила в редакцию:	14 апр. 2026 г.
Принята к публикации:	27 мая 2026 г.
Опубликована в печати:	27 авг. 2026 г.
Опубликована online:	27 авг. 2026 г.

≡ Web of science:	WOS:001861392900001
≡ Scopus:	2-s2.0-105048653262
≡ OpenAlex:	W7204475852