Rathjen, M orcid.org/0000-0003-1699-4778 and Tupailo, S (2020) On the Strength of the Uniform Fixed Point Principle in Intuitionistic Explicit Mathematics. In: Kahle, R and Rathjen, M, (eds.) The Legacy of Kurt Schütte. Springer , pp. 377-399. ISBN 978-3-030-49423-0
Abstract
The paper is concerned with a line of research that plumbs the scope of constructive theories. The object of investigation here is Feferman’s intuitionistic theory of explicit mathematics augmented by the monotone fixed point principle which asserts that every monotone operation on classifications (Feferman’s notion of set) possesses a least fixed point. To be more precise, the new axiom not merely postulates the existence of a least solution, but, by adjoining a newfunctional constant to the language, it is ensured that a fixed point is uniformly presentable as a function of the monotone operation. The strength of the classical non-uniform version, MID, was investigated in [6] whereas that of the uniform version was determined in [16, 17] and shown to be that of subsystems of second order arithmetic based on Π12Π21-comprehension. This involved a rendering of Π12Π21-comprehension in terms of fixed points of non-monotonic Π11Π11-operators and a proof-theoretic interpretation of the latter in specific operator theories that can be interpreted in explicit mathematics with the uniform monotone fixed point principle. The intent of the current paper is to show that the same strength obtains when the underlying logic is taken to be intuitionistic logic.
Metadata
Item Type: | Book Section |
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Copyright, Publisher and Additional Information: | © 2020 Springer Nature Switzerland AG. This is an author produced version of a book chapter published in The Legacy of Kurt Schütte. Uploaded in accordance with the publisher's self-archiving policy. |
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) |
Funding Information: | Funder Grant number John Templeton Foundation (US) 60842 |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Jan 2020 10:12 |
Last Modified: | 16 May 2023 15:47 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/978-3-030-49424-7_19 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:155308 |