The Finitistic Consistency of Heck’s Predicative Fregean System

Notre Dame Journal of Formal Logic 56 (1):61-79 (2015)
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Frege’s theory is inconsistent. 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. We also prove the finitistic consistency of the extension of Heck’s theory to $\Delta^{1}_{1}$-comprehension and of Heck’s ramified predicative second-order system



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Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
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.
The predicative Frege hierarchy.Albert Visser - 2009 - Annals of Pure and Applied Logic 160 (2):129-153.

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