Mathematical Logic Quarterly

Fregean Extensions of First‐Order Theories

Journal Article

Abstract

It is shown by Parsons [2] that the first‐order fragment of Frege's (inconsistent) 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.

Mathematics Subject Classification: 03B10.

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