First-Order Logic: Undecidability and Model Theory *

  • Mordechai Ben-Ari

Abstract

The chapter surveys several important theoretical results in first-order logic. In Sect. 12.1 we prove that validity in first-order logic is undecidable, a result first proved by Alonzo Church. Validity is decidable for several classes of formulas defined by syntactic restrictions on their form (Sect. 12.2). Next, we introduce model theory (Sect. 12.3): the fact that a semantic tableau has a countable number of nodes leads to some interesting results. Finally, Sect. 12.4 contains an overview of Gödel’s surprising incompleteness result.

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Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Mordechai Ben-Ari
    • 1
  1. 1.Department of Science TeachingWeizmann Institute of ScienceRehovotIsrael

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