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Forcings With the Approximation Property

Hannes Jakob

Tuesday, 2023-12-12 14:30

We introduce the approximation property which was implicit in early work of Mitchell and later defined explicitly by Hamkins. In modern set theory, the approximation property has gotten new attention through the ineffable slender list property (ISP), introduced by Weiss in his PhD thesis. In this talk, we give a criterion for the approximation property which is very applicable to variants of Mitchell Forcing, allowing us to obtain several consistency results regarding ISP.