Extensions with the approximation and cover properties have no new large cardinals
arXiv:math/0307229 · doi:10.4064/fm180-3-4
Abstract
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.
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
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