The Tarski-Lindenbaum Algebra of the Class of All Strongly Constructivizable Countable Saturated Models

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• 作者：Mikhail G. Peretyat’kin (19)
  
• 关键词：finitely axiomatizable theory ; Tarski ; Lindenbaum algebra ; c.e. Boolean algebra ; countable saturated model ; computable family of types ; Turing computability ; hierarchy ; m ; complete set
• 刊名：Lecture Notes in Computer Science
• 出版年：2013
• 出版时间：2013
• 年：2013
• 卷：7921
• 期：1
• 页码：353-364
• 全文大小：241KB
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  6. Peretyat’kin, M.G.: Finitely axiomatizable theories. Plenum, New York (1997)
  7. Peretyat’kin, M.G.: On the Tarski-Lindenbaum algebra of the class of all strongly constructivizable prime models. In: Cooper, S.B., Dawar, A., L?we, B. (eds.) CiE 2012. LNCS, vol.?7318, pp. 590-99. Springer, Heidelberg (2012)
  8. Rogers, H.J.: Theory of Recursive Functions and Effective Computability. McGraw-Hill Book Co., New York (1967)
  
• 作者单位：Mikhail G. Peretyat’kin (19)
  
  19. Institute of Mathematics and Mathematical Modeling, 125 Pushkin Street, 050010, Almaty, Kazakhstan
  
• ISSN：1611-3349

文摘

We study the class S s.c of all strongly constructivizable countable saturated models of a finite rich signature σ. We prove that the Tarski-Lindenbaum algebra $\mathcal{L}(S_{s.c})$ considered together with a G?del numbering γ of the sentences is a Boolean $\Sigma^1_1$ -algebra whose computable ultrafilters form a dense set in the set of all ultrafilters; moreover, the Boolean algebra $\mathcal{L}(S_{s.c})$ is universal relative to the class of all Boolean $\Sigma^1_1$ -algebras. This gives an important characterization of the Tarski-Lindenbaum algebra $\mathcal{L}(S_{s.c})$ .