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Forcing is a method first used to prove the continuum hypothesis is independent of the classical axioms of set theory

18 votes

Sheaf-theoretic approach to forcing

It remains to answer Question 2): How is this related to forcing? … It corresponds to the (material) forcing extension by $G$ under translating back-and-forth between structural and material set theory.) Finally, how is all of this related to usual forcing? …
Peter Scholze's user avatar
49 votes
4 answers
7k views

Sheaf-theoretic approach to forcing

If the answer to 1) is Yes, how does this relate to forcing? … In that case, forcing is not supposed to produce new models. …
Peter Scholze's user avatar
10 votes

Condensed / pyknotic sets in terms of forcing over Boolean-valued models of set theory / mul...

Great question — for some reason this tight relation between extremally disconnected profinite sets and forcing had elapsed me! I've just been trying to read a bit about it. … From what I understand, the sheaf-theoretic approach to forcing, as in MacLane-Moerdijk "Sheaves in geometry and logic" Chapter VI, consists of three steps. …
Peter Scholze's user avatar