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On the Consistency of the $\delta_{1}^{1}$-CA Fragment of Frege's "Grundgesetze"

Fernando Ferreira and Kai F. Wehmeier
Journal of Philosophical Logic
Vol. 31, No. 4 (Aug., 2002), pp. 301-311
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226757
Page Count: 11
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On the Consistency of the $\delta_{1}^{1}$-CA Fragment of Frege's "Grundgesetze"
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Abstract

It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Δ₁¹-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case.

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