The Tarski-Lindenbaum algebra of the class of all prime strongly constructivizable models of algorithmic dimension one

We study the class of all prime strongly constructivizable models of algorithmic dimension $1$ 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 $\Pi^0_3$-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 $\Sigma^0_2$-algebras whose computable ultrafilters represent a dense subset in the set of arbitrary ultrafilters in the algebra. This gives a characterization to the Tarski-Lindenbaum algebra of the class of all prime strongly constructivizable models of algorithmic dimension $1$ in a fixed finite rich signature.