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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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The role of univalence in the homotopy interpretation of type theory
In Martin-Löf type theory with identity eliminator
$$
J :
\prod_{B:\prod_{x,y:A}(x=y)\to\mathcal{U}}\left(
\prod_{x:A}B(x,x,\mathrm{refl}_x)\to
\prod_{x,y:A}\prod_{p:x=y}B(x,y,p)
\right)
$$
satisfy …