A Finite First-Order Theory of Classes

  • Florent Kirchner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4502)

Abstract

We expose a formalism that allows the expression of any theory with one or more axiom schemes using a finite number of axioms. These axioms have the property of being easily orientable into rewrite rules. This allows us to give finite first-order axiomatizations of arithmetic and real fields theory, and a presentation of arithmetic in deduction modulo that has a finite number of rewrite rules. Overall, this formalization relies on a weak calculus of explicit substitutions to provide a simple and finite framework.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Florent Kirchner
    • 1
  1. 1.LIX, École Polytechnique, 91128 PalaiseauFrance

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