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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.
1
vote
Homotopy type theory: Are the hierarchy of Type_k universes isomorphic?
The Univalence axiom states that homotopy equivalent types are equal. That doesn't mean the hierarchy is collapsible: that would require judgemental and not Leibniz equality. The very point of HoTT is …
4
votes
The groupoid of algebraic expressions and proofs
I don't have any direct reference for the notion that you are describing, however the notions of $E_n$-algebras and (topological) operads are very close. Firstly, you should note that you need equalit …