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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.
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`Topos' with alternate subobject lattice?
The fact that there is always a Heyting algebra structure on Sub(A) doesn’t exclude the possibility that another lattice structure can coexist with the natural one. As an example take C to be the thre …