The Finitistic Consistency of Heck's Predicative Fregean System

L. Cruz-Filipe; Fernando Ferreira

doi:10.1215/00294527-2835110

The Finitistic Consistency of Heck's Predicative Fregean System

L. Cruz-Filipe
, Fernando Ferreira

Research output: Journal Article or Conference Article in Journal › Journal article › Research › peer-review

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.

Original language	English
Journal	Notre Dame Journal of Formal Logic
Volume	56
Issue number	1
Pages (from-to)	61-79
Number of pages	19
ISSN	0029-4527
DOIs	https://doi.org/10.1215/00294527-2835110
Publication status	Published - 24 Mar 2015
Externally published	Yes

Keywords

Consistency
Fregean arithmetic
Strict predicativity

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10.1215/00294527-2835110

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title = "The Finitistic Consistency of Heck's Predicative Fregean System",

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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AU - Ferreira, Fernando

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N2 - 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.

AB - 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.

KW - Consistency

KW - Fregean arithmetic

KW - Strict predicativity

U2 - 10.1215/00294527-2835110

DO - 10.1215/00294527-2835110

M3 - Journal article

SN - 0029-4527

VL - 56

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EP - 79

JO - Notre Dame Journal of Formal Logic

JF - Notre Dame Journal of Formal Logic

IS - 1

ER -

The Finitistic Consistency of Heck's Predicative Fregean System

Abstract

Keywords

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