Lindström’s Theorems

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

Abstract

In this final chapter we present some results, due to Lindström [25], which we have already mentioned several times. They show that first-order logic occupies a unique place among logical systems. Indeed, we shall prove:
  1. (a)

    There is no logical system with more expressive power than first-order logic, for which both the Compactness Theorem and the Löwenheim-Skolem Theorem hold (Section 3).

     
  2. (b)

    There is no logical system with more expressive power than first-order logic, for which the Löwenheim-Skolem Theorem holds and for which the set of valid sentences is enumerable (Section 4).

     

Keywords

Finite Subset Expressive Power Logical System Computable Function Compactness Theorem 
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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