Journal of Philosophical Logic

, Volume 30, Issue 6, pp 613–616

First-Order Frege Theory is Undecidable

  • Warren Goldfarb
Article

Abstract

The system whose only predicate is identity, whose only nonlogical vocabulary is the abstraction operator, and whose axioms are all first-order instances of Frege's Axiom V is shown to be undecidable.

decidability Frege extensions 

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REFERENCES

  1. Burgess, J. (1998): On a consistent subsystem of Frege's ‘Grundgesetze’, Notre Dame J. Formal Logic 39, 274–278.Google Scholar
  2. Heck, R. (1996): The consistency of predicative fragments of Frege's Grundgesetze der Arithmetik, History and Philosophy of Logic 17, 209–220.Google Scholar
  3. Parsons, T. (1987): On the consistency of the first-order portion of Frege's logical system, Notre Dame J. Formal Logic 28, 161–188; reprinted in W. Demopoulos (ed.), Frege's Philosophy of Mathematics, Harvard Univ. Press, 1995, pp. 422–431.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Warren Goldfarb
    • 1
  1. 1.Department of PhilosophyHarvard UniversityCambridgeU.S.A

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