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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
2
votes
0
answers
111
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Internal characterization of topos validity
I'm using Goldblatt's "Topoi: A categorical analysis of logic" as an introduction to topos logic. At the end of chapter 6, he defines the validity of propositional formulas (I'm not concerned with fir …
15
votes
0
answers
553
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Constructing a topos from a Heyting algebra
It is true that, given any topos $\mathcal{C}$ with a terminal object $1_\mathcal{C}$, $Sub(1_\mathcal{C})$ is a Heyting algebra.
Now suppose that we start with a Heyting algebra $H$. Is it always po …