An Algebraic Characterization of Elementary Equivalence

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

Abstract

The greater part of our exposition so far has been devoted to the development and investigation of first-order logic. We can justify the dominant role assumed by first-order logic in several ways:
  1. (a)

    First-order logic is in principle sufficient for mathematics.

     
  2. (b)

    The intuitive concept of proof and the consequence relation can be adequately described by a formal notion of proof, which is given by means of a calculus.

     
  3. (c)

    A number of semantic results such as the Compactness Theorem or the Löwenheim-Skolem Theorem leads to an enrichment of mathematical methods.

     

Keywords

Elementary Equivalence Winning Strategy Relation Symbol Algebraic Characterization Dense Ordering 
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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