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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > What is a forcing extension (of V)?
What is a forcing extension (of V)?Add to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact webseminars. Mathematical, Foundational and Computational Aspects of the Higher Infinite Recent research into the representability of forcing extensions within ground models has often focussed on semantic formulations; we find definable class models within V that express very closely what it means to be a forcing extension of V (such as Hamkins’ Naturalist Account of Forcing). In this paper, I argue that while this formulation appears to be a good candidate for interpreting forcing over V, it is problematic in that it is unable to interpret theorems concerning objects below a measurable cardinal whilst keeping the ultrapower well-founded, and also encounters difficulties in interpreting class forcings. Instead I suggest that the motivation of a strong class theory (such as MK) over V, combined with a syntactic approach to forcing in a strengthened logic, is able to provide an interpretation of various forcing constructions which does not encounter these difficulties. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:
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