Реферат: First-order formulas reflect an information for semantic and syntactic properties. Links between formulas and properties define their existential and universal interrelations which produce both structural and topological possibilities for characteristics classifying families of semantic and syntactic objects. We adapt general approaches describing links between formulas and properties for families of Abelian groups and their theories defining possibilities for characteristics of formulas and properties including rank values. This adaptation is based on formulas reducing each formula to an appropriate Boolean combination of given ones defining Szmielew invariants for theories of Abelian groups. Using this basedness we describe a trichotomy of possibilities for the rank values of sentences defining neighbourhoods for the set of theories of Abelian groups: the rank can be equal −1, 0, or ∞. Thus the neighbourhoods are either finite or contain continuum many theories. Using the trichotomy we show that each sentence defining a neighbourhood either belongs to finitely many theories or it is generic. We introduce the notion of rich property and generalize the main results for these properties.

Библиографическая ссылка: Павлюк И.И. , Sudoplatov S.V.
Formulas and Properties for Families of Theories of Abelian Groups
Известия Иркутского государственного университета. Серия: Математика (Bulletin of Irkutsk State University. Series Mathematics). 2021. V.36. P.95-109. DOI: 10.26516/1997-7670.2021.36.95 WOS Scopus РИНЦ OpenAlex

Даты:

Поступила в редакцию:	20 апр. 2021 г.
Опубликована в печати:	18 июн. 2021 г.
Опубликована online:	18 июн. 2021 г.

Идентификаторы БД:

Web of science:	WOS:000662709100008
Scopus:	2-s2.0-85109326437
РИНЦ:	46164507
OpenAlex:	W3175078267

Цитирование в БД:

БД	Цитирований
Web of science	7
Scopus	7
РИНЦ	8
OpenAlex	3

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