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

By J. Hamkins. 2003

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/47f691b20bfb5172806cac472358f51303a6180b