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Syntactic Interpretations and Normal Forms

  • H.-D. Ebbinghaus
  • J. Flum
  • W. Thomas
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

In this chapter we collect some results which show to which extent the choice of a symbol set for a mathematical theory is arbitrary. We show, for instance, that the expressive power of first-order languages for group theory does not depend on the choice of S grp or S gr as symbol set. The notion of syntactic interpretation will turn out to be a central concept for our considerations. In the section about normal forms we show that, for different syntactic properties, one can find for each formula a logically equivalent one which has this property, e.g., one which has syntactically an especially simple form.

Keywords

Normal Form Function Symbol Axiom System Atomic Formula Disjunctive Normal Form 
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 1994

Authors and Affiliations

  • H.-D. Ebbinghaus
    • 1
  • J. Flum
    • 1
  • W. Thomas
    • 2
  1. 1.Mathematisches InstitutUniversität FreiburgFreiburgGermany
  2. 2.Institut für Informatik und Praktische MathematikUniversität KielKielGermany

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