THE TARSKI-LINDENBAUM ALGEBRA OF THE CLASS OF PRIME MODELS WITH INFINITE ALGORITHMIC DIMENSIONS HAVING OMEGA-STABLE THEORIES
Peretyatkin M.G. Sudoplatov S.V.
2024Sobolev Institute of Mathematics
Siberian Electronic Mathematical Reports
2024#21Issue 1277 - 292 pp.
We study the class of all prime strongly constructivizable models of infinite algorithmic dimensions having ω-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 $$-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of Boolean $$-algebras. This gives a characterization to the Tarski-Lindenbaum algebra of the class of all prime strongly constructivizable models of infinite algorithmic dimensions having ω-stable theories.
computable isomorphism , prime model , semantic class of models , strongly constructive model , Tarski-Lindenbaum algebra , ω-stable theory
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