arXiv:math/0307229 Abstract

arXiv:math/0307229 [math.LO]Abstract References Reviews Resources

Extensions with the approximation and cover properties have no new large cardinals

Published 2003-07-16, updated 2004-02-24Version 2

If an extension Vbar of V satisfies the delta approximation and cover properties for classes and V is a class in Vbar, then every suitably closed embedding j:Vbar to Nbar in Vbar with critical point above delta restricts to an embedding j|V:V to N amenable to the ground model V. In such extensions, therefore, there are no new large cardinals above delta. This result extends work in math.LO/9808011.

Comments: 25 pages. While preserving the main ideas, the new version makes a number of changes in presentation, such as a new title and reorganized order of results, and corrects an issue concerning definable classes and amenability

Categories: math.LO

Subjects: 03E55, 03E40

Keywords: large cardinals, cover properties, result extends work, delta approximation, extension vbar

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