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

详细信息    查看全文

• 作者：Mikhail G. Peretyat’kin (1) m.g.peretyatkin@predicate-logic.org
• 刊名：Lecture Notes in Computer Science
• 出版年：2012
• 出版时间：2012
• 年：2012
• 卷：7318
• 期：1
• 页码：589-598
• 全文大小：197.5 KB
• 参考文献：1. Goncharov, S.S.: Countable Boolean Algebras and Decidability. Plenum, New York (1997)
  2. Goncharov, S.S., Ershov, Y.L.: Constructive models. Plenum, New York (1999)
  3. Goncharov, S.S., Nurtazin, A.T.: Constructive models of complete decidable theories. Algebra Logika 12(2), 67–77 (1973)
  4. Harrington, L.: Recursively presented prime models. J. Symbolic Logic 39(2), 305–309 (1974)
  5. Hodges, W.: A shorter model theory. Cambridge University Press, Cambridge (1997)
  6. Odintsov, S.P., Selivanov, V.L.: Arithmetical hierarchy and ideals of numerated Boolean algebras. Siberian Math. Journal 30(6), 140–149 (1989) (Russian)
  7. Peretyat’kin, M.G.: Finitely axiomatizable theories. Plenum, New York (1997)
  8. Peretyat’kin, M.G.: On the numerated Boolean algebras with a dense set of computable ultrafilters. Siberian Electronic Mathematical Reports (SEMR), 6 pp. (in publication, 2012)
  9. Rogers, H.J.: Theory of Recursive Functions and Effective Computability. McGraw-Hill Book Co., New York (1967)
• 作者单位：1. Institute of Mathematics, 125 Pushkin Street, 050010 Almaty, Kazakhstan
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

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 L(P_s.c){\mathcal L}(P_{s.c}) considered together with a G?del numbering γ of the sentences is a Boolean P0₄\Pi^0_4-algebra whose computable ultrafilters form a dense set in the set of all ultrafilters; moreover, the numerated Boolean algebra (L(P_s.c),g)({\mathcal L}(P_{s.c}),\gamma) is universal relative to the class of all Boolean S0₃\Sigma^0_3-algebras. This gives an important characterization of the Tarski-Lindenbaum algebra L(P_s.c){\mathcal L}(P_{s.c}) of the semantic class P _s.c.