Conference Paper/Proceeding/Abstract 867 views
Descriptive Set Theory in the Category of Represented Spaces
,
Matthew De Brecht
2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science, Pages: 438 - 449
Swansea University Author:
Arno Pauly
Full text not available from this repository: check for access using links below.
DOI (Published version): 10.1109/lics.2015.48
Abstract
We propose to extend descriptive set theory (DST)beyond its traditional setting of Polish spaces to the representedspaces. There, we can reformulate DST in terms of endofunctorson the categories of represented spaces and computable orcontinuous functions. In particular, this approach satisfies thede...
| Published in: | 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science |
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| ISBN: | 9781479988754 |
| ISSN: | 1043-6871 |
| Published: |
IEEE
2015
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa36020 |
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| Abstract: |
We propose to extend descriptive set theory (DST)beyond its traditional setting of Polish spaces to the representedspaces. There, we can reformulate DST in terms of endofunctorson the categories of represented spaces and computable orcontinuous functions. In particular, this approach satisfies thedemand for a uniform approach to both classic and effectiveDST – computability follows naturally from the setting, ratherthan having to be explicitly demanded.The previous endeavour to extend DST to the Quasi-Polishspaces is subsumed by this work. In several cases the category-theoretic setting enables new, very succinct proofs; and sheds anew light on *why* certain results are true. The framework lets usmake formal some natural questions not easily approachable bytraditional methods. |
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| Keywords: |
descriptive set theory, cartesian closed categories, computable analysis |
| College: |
Faculty of Science and Engineering |
| Start Page: |
438 |
| End Page: |
449 |