Fregean Extensions of First‐Order Theories

Mathematical Logic Quarterly 40 (1):27-30 (1994)
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Abstract

It is shown by Parsons [2] that the first-order fragment of Frege's logical system in the Grundgesetze der Arithmetic is consistent. In this note we formulate and prove a stronger version of this result for arbitrary first-order theories. We also show that a natural attempt to further strengthen our result runs afoul of Tarski's theorem on the undefinability of truth

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10.1002/malq.19940400104

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John L. Bell
University of Western Ontario

Citations of this work

Studies in logical theory.John Dewey - 1903 - New York: AMS Press.
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Frege, Boolos, and logical objects.David J. Anderson & Edward N. Zalta - 2004 - Journal of Philosophical Logic 33 (1):1-26.
Tarski on “essentially richer” metalanguages.David DeVidi & Graham Solomon - 1999 - Journal of Philosophical Logic 28 (1):1-28.

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References found in this work

Frege structures and the notions of truth and proposition.P. Aczel - 1980 - In Stephen Cole Kleene, Jon Barwise, H. Jerome Keisler & Kenneth Kunen, The Kleene Symposium: proceedings of the symposium held June 18-24, 1978 at Madison, Wisconsin, U.S.A. New York: sole distributors for the U.S.A. and Canada, Elsevier North-Holland.

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