Abstract
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 \({\mathcal L}(P_{s.c})\) 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 P s.c.
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Peretyat’kin, M.G. (2012). On the Tarski-Lindenbaum Algebra of the Class of all Strongly Constructivizable Prime Models. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_59
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DOI: https://doi.org/10.1007/978-3-642-30870-3_59
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