Rathjen, M (2017) Proof Theory of Constructive Systems: Inductive Types and Univalence. In: Jaeger, G and Sieg, W, (eds.) Feferman on Foundations: Logic, Mathematics, Philosophy. Outstanding Contributions to Logic . Springer , pp. 385-419. ISBN 978-3-319-63332-9
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-Löf 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-Löf type theory.
Metadata
Item Type: | Book Section |
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Authors/Creators: |
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Editors: |
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Keywords: | Explicit mathematics; Constructive Zermelo-Fraenkel set theory; Martin-Löf type theory; Univalence axiom; Proof-theoretic strength |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Oct 2016 14:23 |
Last Modified: | 24 Aug 2018 13:40 |
Published Version: | http://www.springer.com/gb/book/9783319633329 |
Status: | Published |
Publisher: | Springer |
Series Name: | Outstanding Contributions to Logic |
Identification Number: | 10.1007/978-3-319-63334-3 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:106000 |