The consistency of predicative fragments of Frege's Grundgesetze der Arithmetik

History and Philosophy of Logic 17 (1):209-220 (1996)
Abstract
As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell?s Paradox being derivable in it.This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege?s Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is relatively interpretable in the simple predicative fragment. The philosophical significance of the result is discussed
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DOI 10.1080/01445349608837265
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References found in this work BETA
On the Consistency of the First-Order Portion of Frege's Logical System.Terence Parsons - 1987 - Notre Dame Journal of Formal Logic 28 (1):161-168.
Fregean Extensions of First‐Order Theories.John L. Bell - 1994 - Mathematical Logic Quarterly 40 (1):27-30.

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Citations of this work BETA
Modality and Paradox.Gabriel Uzquiano - 2015 - Philosophy Compass 10 (4):284-300.
Comparing Peano Arithmetic, Basic Law V, and Hume’s Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.
Predicative Fragments of Frege Arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Bad Company Tamed.Øystein Linnebo - 2009 - Synthese 170 (3):371 - 391.

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