This article is cited in 1 paper

Mathematical logic, algebra and number theory

The Tarski–Lindenbaum algebra of the class of prime models with infinite algorithmic dimensions having omega-stable theories

M. G. Peretyat'kin

Institute of Mathematics and Mathematical Modeling, Shevchenko 28, 050010, Almaty, Kazakhstan

Abstract: We study the class of all prime strongly constructivizable models of infinite algorithmic dimensions having $\omega$-stable theories in a fixed finite rich signature. It is proved that the Tarski-Lindenbaum algebra of this class considered together with a Gödel numbering of the sentences is a Boolean $\Sigma^1_1$-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of Boolean $\Sigma^1_1$-algebras. This gives a characterization to the Tarski–Lindenbaum algebra of the class of all prime strongly constructivizable models of infinite algorithmic dimensions having $\omega$-stable theories.

Keywords: Tarski–Lindenbaum algebra, strongly constructive model, computable isomorphism, semantic class of models, $\omega$-stable theory, prime model.

UDC: 510.67

MSC: 03B10, 03D35

Received December 14, 2023, published April 8, 2024

Language: English

DOI: 10.33048/semi.2024.21.021