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The Meaning of Clauses

  • Daniele Mundici
Part of the UNITEXT book series (UNITEXT)

Abstract

The discovery of a non-Euclidean geometry ended a two thousand-year-old search for a refutation of the set of statements obtained by adding the negation of the Fifth Postulate (about parallel lines) to the remaining Euclidean axioms. This is an important example of a general fact: if there exists a possible world in which a set of statements is true, then there does not exist a refutation of this set of statements. The reverse implication is a fundamental result of logic, the completeness theorem of Gödel, for the proof of which we cannot content ourselves with a generic intuition. Instead, we have to learn to work with some fundamental concepts that will be defined in this chapter.

Keywords

Logical Consequence Propositional Logic Fundamental Concept Fundamental Result Predicate Logic 
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.

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Daniele Mundici
    • 1
  1. 1.Department of Mathematics and Computer Science “U. Dini”University of FlorenceItaly

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