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A Reduction of the NF consistency Problem

Published online by Cambridge University Press:  12 March 2014

Athanassios Tzouvaras
Athanassios Tzouvaras*
Affiliation:
Aristotle University of Thessaloniki, Department of Mathematics 541 24 Thessaloniki, Greece. E-mail: tzouvara@math.auth.gr
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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 1-extendible coherent pairs.

Keywords

New Foundationstype-shifting automorphismforcingcoherent pairn-extendible coherent pair
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 285 - 304
Copyright
Copyright © Association for Symbolic Logic 2007

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References

REFERENCES

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