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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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Online
ISSN
1898-9934
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Volume 20, Issue 3 (Dec 2012)

Issues

The Gödel Completeness Theorem for Uncountable Languages

Julian J. Schlöder
  • Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, D-53113 Bonn, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Peter Koepke
  • Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, D-53113 Bonn, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-02-02 | DOI: https://doi.org/10.2478/v10037-012-0023-z

Summary

This article is the second in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [15] for uncountably large languages. We follow the proof given in [16]. The present article contains the techniques required to expand a theory such that the expanded theory contains witnesses and is negation faithful. Then the completeness theorem follows immediately.

  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Google Scholar

  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Google Scholar

  • [3] Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.Google Scholar

  • [4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Google Scholar

  • [5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Google Scholar

  • [6] Patrick Braselmann and Peter Koepke. Equivalences of inconsistency and Henkin models. Formalized Mathematics, 13(1):45-48, 2005.Google Scholar

  • [7] Patrick Braselmann and Peter Koepke. G¨odel’s completeness theorem. Formalized Mathematics, 13(1):49-53, 2005.Google Scholar

  • [8] Patrick Braselmann and Peter Koepke. A sequent calculus for first-order logic. FormalizedMathematics, 13(1):33-39, 2005.Google Scholar

  • [9] Patrick Braselmann and Peter Koepke. Substitution in first-order formulas. Part II. The construction of first-order formulas. Formalized Mathematics, 13(1):27-32, 2005.Google Scholar

  • [10] Czesław Bylinski. A classical first order language. Formalized Mathematics, 1(4):669-676, 1990.Google Scholar

  • [11] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Google Scholar

  • [12] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Google Scholar

  • [13] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Google Scholar

  • [14] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Google Scholar

  • [15] Kurt G¨odel. Die Vollst¨andigkeit der Axiome des logischen Funktionenkalk¨uls. Monatshefte f¨ur Mathematik und Physik 37, 1930.Google Scholar

  • [16] W. Thomas H.-D. Ebbinghaus, J. Flum. Einf¨uhrung in die Mathematische Logik. Springer-Verlag, Berlin Heidelberg, 2007.Google Scholar

  • [17] Piotr Rudnicki and Andrzej Trybulec. A first order language. Formalized Mathematics, 1(2):303-311, 1990.Google Scholar

  • [18] Julian J. Schlöder and Peter Koepke. Transition of consistency and satisfiability under language extensions. Formalized Mathematics, 20(3):193-197, 2012, doi: 10.2478/v10037-012-0022-0.CrossrefGoogle Scholar

  • [19] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.Google Scholar

  • [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

  • [21] Edmund Woronowicz. Interpretation and satisfiability in the first order logic. FormalizedMathematics, 1(4):739-743, 1990.Google Scholar

  • [22] Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.Google Scholar

  • [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Google Scholar

About the article

This article is part of the first author’s Bachelor thesis under the supervision of the second author.


Published Online: 2013-02-02

Published in Print: 2012-12-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0023-z.

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