On the Tarski-Lindenbaum Algebra of the Class of all Strongly Constructivizable Prime Models

摘要

We study the class P_(s.c) of all strongly constructivizable prime models of a finite rich signature σ. It is proven that the Tarski-Lindenbaum algebra L(P_(s.c)) considered together with a Goedel numbering γ of the sentences is a Boolean Π_4~0-algebra whose computable ultrafilters form a dense set in the set of all ultrafilters; moreover, the numerated Boolean algebra (L(P_(s.c)),γ) is universal relative to the class of all Boolean ∑_3~0-algebras. This gives an important characterization of the Tarski-Lindenbaum algebra L(P_(s.c)) of the semantic class P_(s.c).