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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.

2 votes
1 answer
545 views

Higher inductive types in higher observational type theory

Mike Shulman gave the following set of talks on higher observational type theory earlier this year (part 1, part 2, part 3). However, while he talked about how the identity types are defined and behav …
Madeleine Birchfield's user avatar
3 votes
0 answers
277 views

Principle of unique choice in homotopy type theory

In the MathOverflow thread Mathematics without the principle of unique choice, Mike Shulman defines the principle of unique choice to be if $R$ is a relation between two sets $A$, $B$, and for every …
Madeleine Birchfield's user avatar
5 votes

Consistency of Generalised Continuum Hypothesis and univalence in HoTT

Dominik Kirst and Felix Rech managed to formalize the Generalized Continuum Hypothesis for sets in the HoTT library in Coq with univalence, which already shows the consistency of the GCH with univalen …
Madeleine Birchfield's user avatar