Abstract: In a series of papers various approximations of infinite structures by finite ones, i.e. pseudofiniteness are studied [1, 2, 3, 4] including finite approximations of strongly minimal structures [5]. We continue to study possibilities of approximations of theories with respect to given families of theories [6, 7, 8]. At the present paper we consider and describe some possibilities of approximations by strongly minimal structures and theories. Some kinds of approximating formulae in this case are described, too. For theories of signatures Σ1 without non-trivial definable n -ary relations, for n > 1, we prove a trichotomy theorem according to which each such theory either belongs to the class of theories with finite models, or belongs to the class of strongly minimal theories, or belongs to the class of pseudo-strongly-minimal theories. The last two cases are united by the class of pseudofinite theories. That trichotomy shows that each signature with unary predicates has a pseudo-strongly-minimal theory. It confirms that the class of pseudo-strongly-minimal theories starts by signatures with at least one n -ary predicate or function, for n ≥ 1.

Cite: Kulpeshov B.S. , Pavlyuk I.I. , Sudoplatov S.V.
On pseudo-strongly-minimal formulae, structures and theories
In compilation Model Theory and Algebra 2024: Collection of papers. – НГТУ., 2024. – C.42-47. – ISBN 978-5-7782-5285-1. РИНЦ

Dates:

Submitted:	Oct 1, 2024
Accepted:	Oct 31, 2024
Published print:	Nov 8, 2024
Published online:	Nov 8, 2024

Identifiers:

Elibrary:

75128131

Citing:

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