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On the constructive and computational content of abstract mathematics

Ulrich Berger Orcid Logo

Mathesis Universalis, Computability and Proof, Volume: Synthese Library - Studies in Epistemology, Logic, Methodology, and Philosophy of Science

Swansea University Author: Ulrich Berger Orcid Logo

Abstract

This essay describes an approach to constructive mathematics based on abstract i.e. axiomatic mathematics. Rather than insisting on structures to be explicitly constructed, constructivity is dened by the sole requirement that proofs have computational content. It is shown that this approach is compa...

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Published in: Mathesis Universalis, Computability and Proof
Published: 2019
URI: https://cronfa.swan.ac.uk/Record/cronfa50301
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first_indexed 2019-05-13T10:26:30Z
last_indexed 2019-10-01T14:16:51Z
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spelling 2019-10-01T11:50:58.4880843 v2 50301 2019-05-09 On the constructive and computational content of abstract mathematics 61199ae25042a5e629c5398c4a40a4f5 0000-0002-7677-3582 Ulrich Berger Ulrich Berger true false 2019-05-09 SCS This essay describes an approach to constructive mathematics based on abstract i.e. axiomatic mathematics. Rather than insisting on structures to be explicitly constructed, constructivity is dened by the sole requirement that proofs have computational content. It is shown that this approach is compatible with restricted forms of classical logic and choice principles. Book chapter Mathesis Universalis, Computability and Proof Synthese Library - Studies in Epistemology, Logic, Methodology, and Philosophy of Science constructive mathematics, realizability, program extraction, choice principles 27 8 2019 2019-08-27 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2019-10-01T11:50:58.4880843 2019-05-09T22:55:52.1594745 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Ulrich Berger 0000-0002-7677-3582 1
title On the constructive and computational content of abstract mathematics
spellingShingle On the constructive and computational content of abstract mathematics
Ulrich Berger
title_short On the constructive and computational content of abstract mathematics
title_full On the constructive and computational content of abstract mathematics
title_fullStr On the constructive and computational content of abstract mathematics
title_full_unstemmed On the constructive and computational content of abstract mathematics
title_sort On the constructive and computational content of abstract mathematics
author_id_str_mv 61199ae25042a5e629c5398c4a40a4f5
author_id_fullname_str_mv 61199ae25042a5e629c5398c4a40a4f5_***_Ulrich Berger
author Ulrich Berger
author2 Ulrich Berger
format Book chapter
container_title Mathesis Universalis, Computability and Proof
container_volume Synthese Library - Studies in Epistemology, Logic, Methodology, and Philosophy of Science
publishDate 2019
institution Swansea University
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
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description This essay describes an approach to constructive mathematics based on abstract i.e. axiomatic mathematics. Rather than insisting on structures to be explicitly constructed, constructivity is dened by the sole requirement that proofs have computational content. It is shown that this approach is compatible with restricted forms of classical logic and choice principles.
published_date 2019-08-27T04:01:43Z
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