Warning: I have run out of easy topics in category theory, so I'm going to introduce Homotopy Type Theory for programmers. Can't let mathematicians have all the fun. https://t.co/wuExChh5pa

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract We introduce an extension of Martin-L"of type theory, which we conjecture to have the same proof theoretic strength as Kripke-Platek set theory (KP) extended by one \Pi 3-reflecting ordinal and finitely many admissibles above it. That would mean that the proof theoretic strength of this type theory is substantially bigger than that of any previous predicatively justified extensions of Martin-L"of type theory, including the Mahlo universe. The universe is constructed following the principles of ordinal notation systems of strength KP plus one \Pi 3-reflecting ordinal, therefore extracting key ideas of these notation systems. We introduce a model for this type theory, and determine an upper bound for its proof theoretic strength. This article only presents the main ideas of this model construction, full details will be given in a future article. 1 Introduction This article is a step in a research programme of the author with the…