The Tarski–Lindenbaum algebra of the class of strongly constructivizable models with ω-stable theories
Peretyat’kin M.
February 2025Springer Science and Business Media Deutschland GmbH
Archive for Mathematical Logic
2025#64Issue 167 - 78 pp.
We study the class of all strongly constructivizable models 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 Σ11-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 all Boolean Σ11-algebras. This gives a characterization to the Tarski-Lindenbaum algebra of the class of all strongly constructivizable models with ω-stable theories.
Computable isomorphism , Model with ω-stable theory , Semantic class of models , Strongly constructive model , Tarski–Lindenbaum algebra
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