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The Scope of First-Order Logic

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

Abstract

In Chapter I we realized that investigations into the logical reasoning used in mathematics require an analysis of the concepts of mathematical proposition and proof. In undertaking such an analysis, we were led to introduce the first-order languages. We also defined a notion of formal proof which corresponds to the intuitive concept of mathematical proof. The Completeness Theorem then shows that every proposition which is mathematically provable from a system of axioms (and thus follows from it) can also be obtained by means of a formal proof, provided the proposition and the system of axioms admit a first-order formulation.

Keywords

Formal Proof Continuum Hypothesis Sequent Calculus Completeness Theorem Sequent Rule 
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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