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

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.