×

zbMATH — the first resource for mathematics

A reduction of the NF consistency problem. (English) Zbl 1116.03046
Summary: 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.

MSC:
03E70 Nonclassical and second-order set theories
03E35 Consistency and independence results
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Proceedings of the International Congress, Stanford, 1960 pp 116–124– (1962)
[2] Set theory with a universal set 20 (1992)
[3] Soviet Mathematics Doklady 10 pp 1387–1390– (1969)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.