Russell's paradox in consistent fragments of Frege's grundgesetze der arithmetik

In Godehard Link (ed.), One Hundred Years of Russell’s Paradox. de Gruyter (2004)

Kai Wehmeier
University of California, Irvine
We provide an overview of consistent fragments of the theory of Frege’s Grundgesetze der Arithmetik that arise by restricting the second-order comprehension schema. We discuss how such theories avoid inconsistency and show how the reasoning underlying Russell’s paradox can be put to use in an investigation of these fragments.
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Comparing Peano Arithmetic, Basic Law V, and Hume’s Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.

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