A Reduction of the NF Consistency Problem

Journal of Symbolic Logic 72 (1):285 - 304 (2007)
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Abstract

We give a necessary and sufficient condition in order that a type-shifting automorphism be constructed on a model of the Theory of Simple Types (TST) by forcing. Namely it is proved that, if for every n ≥ 1 there is a model of TST in the ground model M of ZFC that contains an n-extendible coherent pair, then there is a generic extension M[G] of M that contains a model of TST with a type-shifting automorphism, and hence M[G] contains a model of NF. The converse holds trivially. It is also proved that there exist models of TST containing l-extendible coherent pairs

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Athanassios Tzouvaras
Aristotle University of Thessaloniki (PhD)

Citations of this work

Decreasing sentences in Simple Type Theory.Panagiotis Rouvelas - 2017 - Mathematical Logic Quarterly 63 (5):342-363.
Increasing sentences in Simple Type Theory.Panagiotis Rouvelas - 2017 - Annals of Pure and Applied Logic 168 (10):1902-1926.

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