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2012 | 20 | 3 | 199-203
Tytuł artykułu

The Gödel Completeness Theorem for Uncountable Languages

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
3
Strony
199-203
Opis fizyczny
Daty
wydano
2012-12-01
online
2013-02-02
Twórcy
  • Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, D-53113 Bonn, Germany
autor
  • Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, D-53113 Bonn, Germany
Bibliografia
  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [3] Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.
  • [4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [6] Patrick Braselmann and Peter Koepke. Equivalences of inconsistency and Henkin models. Formalized Mathematics, 13(1):45-48, 2005.
  • [7] Patrick Braselmann and Peter Koepke. G¨odel’s completeness theorem. Formalized Mathematics, 13(1):49-53, 2005.
  • [8] Patrick Braselmann and Peter Koepke. A sequent calculus for first-order logic. FormalizedMathematics, 13(1):33-39, 2005.
  • [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.
  • [10] Czesław Bylinski. A classical first order language. Formalized Mathematics, 1(4):669-676, 1990.
  • [11] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [12] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [13] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [14] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [15] Kurt G¨odel. Die Vollst¨andigkeit der Axiome des logischen Funktionenkalk¨uls. Monatshefte f¨ur Mathematik und Physik 37, 1930.
  • [16] W. Thomas H.-D. Ebbinghaus, J. Flum. Einf¨uhrung in die Mathematische Logik. Springer-Verlag, Berlin Heidelberg, 2007.
  • [17] Piotr Rudnicki and Andrzej Trybulec. A first order language. Formalized Mathematics, 1(2):303-311, 1990.
  • [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.[Crossref]
  • [19] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
  • [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [21] Edmund Woronowicz. Interpretation and satisfiability in the first order logic. FormalizedMathematics, 1(4):739-743, 1990.
  • [22] Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.
  • [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-012-0023-z
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