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Descriptive Set Theory in the Category of Represented Spaces / Arno Pauly; Matthew De Brecht

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science, Pages: 438 - 449

Swansea University Author: Arno, Pauly

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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...

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Published in: 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
ISBN: 9781479988754
ISSN: 1043-6871
Published: IEEE 2015
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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.
Keywords: descriptive set theory, cartesian closed categories, computable analysis
College: College of Science
Start Page: 438
End Page: 449