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Mathematical logic, algebra and number theory

The Tarski-Lindenbaum algebra of the class of all prime strongly constructivizable models of algorithmic dimension one

M. G. Peretyat'kin

Institute of Mathematics and Mathematical Modeling, 125, Pushkin str., Almaty, 050010, Kazakhstan

Abstract: We study the class of all prime strongly constructivizable models of algorithmic dimension $1$ 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 $\Pi^0_3$-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 $\Sigma^0_2$-algebras whose computable ultrafilters represent a dense subset in the set of arbitrary ultrafilters in the algebra. This gives a characterization to the Tarski-Lindenbaum algebra of the class of all prime strongly constructivizable models of algorithmic dimension $1$ in a fixed finite rich signature.

Keywords: first-order logic, Tarski-Lindenbaum algebra, computable isomorphism, semantic class of models, algorithmic complexity estimate.

UDC: 510.67

MSC: 03B10, 03D35

Received April 2, 2020, published July 9, 2020

Language: English

DOI: 10.33048/semi.2020.17.067

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