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Completeness Theorem for First-Order Logic

  • Shashi Mohan Srivastava
Chapter
Part of the Universitext book series (UTX)

Abstract

In Chap. 1, we described what a first-order language is and what its terms and formulas are. We fixed a first-order language L. In Chap. 2, we described the semantics of first-order languages. In Chap. 3, we considered a simpler form of logic – propositional logic, defined what a proof is in that logic, and proved its completeness theorem. In this chapter we shall define proof in a first-order theory and prove the corresponding completeness theorem. The result for countable theories was first proved by Gödel in 1930. The result in its complete generality was first observed by Malcev in 1936. The proof given below is due to Leo Henkin.

Keywords

Propositional Logic Completeness Theorem Canonical Structure Constant Symbol Truth Valuation 
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 Science+Business Media New York 2013

Authors and Affiliations

  • Shashi Mohan Srivastava
    • 1
  1. 1.Indian Statistical InstituteKolkataIndia

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