2022-05-26: Fredrik Nordvall Forsberg (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Fredrik Nordvall Forsberg (MSP)

Constructive Ordinal Theory in Homotopy Type Theory

Abstract

Many constructions proceed in stages: we give a base case, a step case showing how to go from stage n to stage n+1, and then the desired result is achieved in the limit. In more complicated situations, we have to go beyond stages indexed by natural numbers to stages indexed by larger structures — ordinals, a cornerstone of modern mathematics. These are well understood classically, but less so in a constructive setting, where different equivalent classical notions split apart, with different advantages and disadvantages for each. I will show how a theory of different ordinals can be developed constructively in the setting of homotopy type theory, and how modern type-theoretic features such as higher inductive types and inductive-inductive definitions can be used to construct ordinal notation systems that truly behave like ordinals, with extensional and wellfounded order relations.

Joint work with Nicolai Kraus and Chuangjie Xu.

2022-05-26 14:00:00 UTC
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