Maietti, ME, Maschio, S and Rathjen, M (2021) A realizability semantics for inductive formal topologies, church’s thesis and axiom of choice. Logical Methods in Computer Science, 17 (2). 21:1-21:21. ISSN 1860-5974
Abstract
We present a Kleene realizability semantics for the intensional level of the Minimalist Foundation, for short mtt, extended with inductively generated formal topologies, Church's thesis and axiom of choice. This semantics is an extension of the one used to show consistency of the intensional level of the Minimalist Foundation with the axiom of choice and formal Church's thesis in previous work. A main novelty here is that such a semantics is formalized in a constructive theory represented by Aczel's constructive set theory CZF extended with the regular extension axiom.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © M. E. Maietti, S. Maschio, and M. Rathjen. This work is licensed under the Creative Commons Attribution License. To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/ or send a letter to Creative Commons, 171 Second St, Suite 300, San Francisco, CA 94105, USA, or Eisenacher Strasse 2, 10777 Berlin, Germany. |
Keywords: | Mathematics; Logic |
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: | 24 Jun 2021 10:46 |
Last Modified: | 25 Jun 2023 22:41 |
Status: | Published |
Publisher: | Logical Methods in Computer Science |
Identification Number: | 10.23638/LMCS-17(2:21)2021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:175519 |