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Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type theory.
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HoTT without Funext, Univalence
Are there any models of Martin-Löf's intensional type theory in which univalence or function extensionality fails?
In the HoTT book, axioms like $\mathsf{LEM}_{\infty}$ (in Section 3.4) are proved to …