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

  • Mikhail G. Peretyat’kin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)


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.


Boolean Algebra Prime Model Maximal Chain Principal Type Semantic Class 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mikhail G. Peretyat’kin
    • 1
  1. 1.Institute of MathematicsAlmatyKazakhstan

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