Model companion properties of some theories
Abstrak
The class K of algebraic systems of signature σ is called a formula-definable class if there exists an algebraic system A of signature σ such that for any algebraic system B of signature σ it is B ∈ K if and only if Th(B) · Th(A) = Th(A). The paper shows that the formula-definable class of algebraic systems is idempotently formula-definable and is an axiomatizable class of algebraic systems. Any variety of algebraic systems is an idempotently formula-definite class. If the class K of all existentially closed algebraic systems of a theory T is formula-definable, then a theory of the class K is a model companion of the theory T. Also, in the paper the examples of some theories on the properties of formula-definability, pseudofiniteness and smoothly approximability of their model companion were discussed.
Topik & Kata Kunci
Penulis (4)
А. Кабиденов
А. Касатова
М.И. Бекенов
Н.Д. Мархабатов
Akses Cepat
- Tahun Terbit
- 2024
- Sumber Database
- DOAJ
- DOI
- 10.31489/2024m2/114-123
- Akses
- Open Access ✓