The Finitistic Consistency of Heck's Predicative Fregean System
- L. Cruz-Filipe,
- Fernando Ferreira
- University of Southern Denmark,
- University of Lisbon
Research Output:
Journal Article or Conference Article in Journal
Journal article
Peer-review
Open access
Publication Information
Output type
Research Output:
Journal Article or Conference Article in Journal
Journal article
Peer-reviewOriginal language
EnglishPages from-to (Number of pages)
Pages 61-79 (19 pages)Journal (Volume, Issue Number)
Notre Dame Journal of Formal Logic (Volume 56, Issue 1)Publication milestones
- Published - 24/03/2015
Publication status
Published - 24/03/2015
ISSN
0029-4527Publication IDs
- Scopus: 84926657639
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.
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