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

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

2003-07-16

arxiv.org/abs/math/0307229v2

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Logic

25 pages. While preserving the main ideas, the new version makes a number of changes in presentation, such as a new title and

Scientific paper

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.

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