Book chapter 1233 views
On the constructive and computational content of abstract mathematics
Ulrich Berger
Mathesis Universalis, Computability and Proof, Volume: Synthese Library - Studies in Epistemology, Logic, Methodology, and Philosophy of Science
Swansea University Author: Ulrich Berger
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...
| Published in: | Mathesis Universalis, Computability and Proof |
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| Published: |
2019
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa50301 |
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2019-05-13T10:26:30Z |
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2019-10-01T14:16:51Z |
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cronfa50301 |
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SURis |
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2019-10-01T11:50:58.4880843 v2 50301 2019-05-09 On the constructive and computational content of abstract mathematics 61199ae25042a5e629c5398c4a40a4f5 Ulrich Berger Ulrich Berger true false 2019-05-09 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 COLLEGE CODE 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 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 |
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61199ae25042a5e629c5398c4a40a4f5 |
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61199ae25042a5e629c5398c4a40a4f5_***_Ulrich Berger |
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Ulrich Berger |
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Ulrich Berger |
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Book chapter |
| container_title |
Mathesis Universalis, Computability and Proof |
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Synthese Library - Studies in Epistemology, Logic, Methodology, and Philosophy of Science |
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2019 |
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Swansea University |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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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 |
2019-08-27T04:37:43Z |
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1851366481408819200 |
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11.089572 |