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Questions taking place in the category of locales, which is given by the opposite of the category of frames. Also appropriate for questions about pointless topology.
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Is it possible to completely embed complete Heyting algebras into upsets of a poset?
Let $H$ be a Heyting algebra. It is a well-known result that there is a partially ordered set (Kripke frame) $X$ such that there is an embedding of Heyting algebras $f: H \to \mathsf{Up}(X)$, where $\ …