Amending Frege's "Grundgesetze der Arithmetik" to the Memory of Nhê (1925-2001)

Synthese 147 (1):3 - 19 (2005)
Frege's "Grundgesetze der Arithmetik" is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege's Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the "Grundgesetze" is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this extended system.
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DOI 10.2307/20118645
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Richard Heck (1997). Grundgesetze der Arithmetik I §§29‒32. Notre Dame Journal of Formal Logic 38 (3):437-474.

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