Proof Theory of Constructive Systems: Inductive Types and Univalence [article]

Michael Rathjen
2018 arXiv   pre-print
In Feferman's work, explicit mathematics and theories of generalized inductive definitions play a central role. One objective of this article is to describe the connections with Martin-Lof type theory and constructive Zermelo-Fraenkel set theory. Proof theory has contributed to a deeper grasp of the relationship between different frameworks for constructive mathematics. Some of the reductions are known only through ordinal-theoretic characterizations. The paper also addresses the strength of
more » ... vodsky's univalence axiom. A further goal is to investigate the strength of intuitionistic theories of generalized inductive definitions in the framework of intuitionistic explicit mathematics that lie beyond the reach of Martin-Lof type theory.
arXiv:1610.02191v2 fatcat:poqgfttkgjfrxo5yvpohajq7zq