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Failures of the Forcing Theorem

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Mathematical, Foundational and Computational Aspects of the Higher Infinite

The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a condition in the relevant generic filter. We show that both the definability of the forcing relation and the truth lemma can fail for class forcing. We will also present positive results about and characterizations of the forcing theorem in class forcing. This is joint work with Regula Krapf, Philipp Lcke, Ana Njegomir and Philipp Schlicht.

This talk is part of the Isaac Newton Institute Seminar Series series.

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