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)

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.

Keywords

Boolean Algebra Prime Model Maximal Chain Principal Type Semantic Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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