On the tarski-lindenbaum algebra of the class of all strongly constructivizable prime models

• Authors: Mikhail G. Peretyat'kin
• Venue: CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
• Year: 2012

We study the class Ps.c of all strongly constructivizable prime models of a finite rich signature σ. It is proven that the Tarski-Lindenbaum algebra ${\mathcal L}(P_{s.c})$ considered together with a Gödel numbering γ of the sentences is a Boolean $\Pi^0_4$-algebra whose computable ultrafilters form a dense set in the set of all ultrafilters; moreover, the numerated Boolean algebra $({\mathcal L}(P_{s.c}),\gamma)$ is universal relative to the class of all Boolean $\Sigma^0_3$-algebras. This gives an important characterization of the Tarski-Lindenbaum algebra ${\mathcal L}(P_{s.c})$ of the semantic class Ps.c.