Proof Theory of Constructive Systems: Inductive Types and Univalence

Michael Rathjen

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arXiv · 1610.02191

Proof Theory of Constructive Systems: Inductive Types and Univalence

Michael Rathjen

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Abstract

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 Voevodsky'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.

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Michael Rathjen. 2016-10-07. Proof Theory of Constructive Systems: Inductive Types and Univalence. https://arxiv.org/abs/1610.02191

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