Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-16T23:25:31.658Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Forster, T. E., Set theory with a universal set, Oxford Logic Guides, vol. 20, Oxford University Press, 1992.Google Scholar
[2]Grishin, V. N., Consistency of a fragment of Quine's NF system, Soviet Mathematics Doklady, vol. 10 (1969), no. 6, pp. 1387–1390.Google Scholar
[3]Grishin, V. N., The method of stratification in set theory, Ph.D. thesis, Moscow University, 1972, in Russian.Google Scholar
[4]Specker, E., Typical ambiguity, Proceedings of the International Congress, Stanford, 1960, Logic Methodology and Philosophy of Science, Stanford University Press, 1962, pp. 116–124.Google Scholar