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

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.

preprint2004arXivOpen access
Joel David Hamkins
math.LO
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Joel David Hamkins

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