Abstract
We study the class of all prime strongly constructivizable models of innite algorithmic dimensions having ω-stable theories in a xed nite rich signature.It is proved that the Tarski-Lindenbaum algebra of this class considered together with a G odel numbering of the sentences is a Boolean Σ 1 1 -algebra whose computable ultralters form a dense subset in the set of all ultralters; moreover, this algebra is universal with respect to the class of Boolean Σ 1 1 -algebras.This gives a characterization to the Tarski-Lindenbaum algebra of the class of all prime strongly constructivizable models of innite algorithmic dimensions having ω-stable theories.