On the consistency of the Δ11-CA fragment of Frege's grundgesetze

Journal of Philosophical Logic 31 (4):301-311 (2002)
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.
Keywords comprehension  consistency proofs  Frege  recursive saturation  Russell's paradox  second-order logic  value range
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DOI 10.1023/A:1019919403797
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Gabriel Uzquiano (2015). Modality and Paradox. Philosophy Compass 10 (4):284-300.

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