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On the Consistency of the Δ1 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 Δ1 1-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Lisboa, Rua Ernesto Vasconcelos, C1-3, 1749-016, Lisboa, Portugal

    Fernando Ferreira & Kai F. Wehmeier

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  1. Fernando Ferreira
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  2. Kai F. Wehmeier
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Ferreira, F., Wehmeier, K.F. On the Consistency of the Δ1 1-CA Fragment of Frege's Grundgesetze . Journal of Philosophical Logic 31, 301–311 (2002). https://doi.org/10.1023/A:1019919403797

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  • DOI: https://doi.org/10.1023/A:1019919403797

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