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2015 The Finitistic Consistency of Heck’s Predicative Fregean System
Luís Cruz-Filipe, Fernando Ferreira
Notre Dame J. Formal Logic 56(1): 61-79 (2015). DOI: 10.1215/00294527-2835110

Abstract

Frege’s theory is inconsistent (Russell’s paradox). However, the predicative version of Frege’s system is consistent. This was proved by Richard Heck in 1996 using a model-theoretic argument. In this paper, we give a finitistic proof of this consistency result. As a consequence, Heck’s predicative theory is rather weak (as was suspected). We also prove the finitistic consistency of the extension of Heck’s theory to Δ11-comprehension and of Heck’s ramified predicative second-order system.

Citation

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Luís Cruz-Filipe. Fernando Ferreira. "The Finitistic Consistency of Heck’s Predicative Fregean System." Notre Dame J. Formal Logic 56 (1) 61 - 79, 2015. https://doi.org/10.1215/00294527-2835110

Information

Published: 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1356.03101
MathSciNet: MR3326589
Digital Object Identifier: 10.1215/00294527-2835110

Subjects:
Primary: 03F25, 03F35
Secondary: 03A05, 03B30, 03F05

Rights: Copyright © 2015 University of Notre Dame

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Vol.56 • No. 1 • 2015
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