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March 2007 A reduction of the NF consistency problem
Athanassios Tzouvaras
J. Symbolic Logic 72(1): 285-304 (March 2007). DOI: 10.2178/jsl/1174668396

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 $n \geq 1$ 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 1-extendible coherent pairs.

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Athanassios Tzouvaras. "A reduction of the NF consistency problem." J. Symbolic Logic 72 (1) 285 - 304, March 2007. https://doi.org/10.2178/jsl/1174668396

Information

Published: March 2007
First available in Project Euclid: 23 March 2007

zbMATH: 1116.03046
MathSciNet: MR2298483
Digital Object Identifier: 10.2178/jsl/1174668396

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 1 • March 2007
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