Compact metrizable structures and classification problems

Rosendal, Christian; Zielinski, Joseph

doi:10.48550/arxiv.1610.00370

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2018

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“…Independently from us, Rosendal and Zielinski [10,Prop. 10 and 11] established classifiability by countable structures for the isomorphism relation in the four classes above, and posted their result on arXiv in Oct. 2016.…”

Section: Introductionmentioning

confidence: 96%

The Complexity of Topological Group Isomorphism

Kechris¹,

Nies²,

Tent³

2018

J. symb. log.

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We study the complexity of the topological isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducibility between equivalence relations on Borel spaces. For profinite, locally compact, and Roelcke precompact groups, we show that the complexity is the same as the one of countable graph isomorphism. For oligomorphic groups, we merely establish this as an upper bound.

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Section: Introductionmentioning

confidence: 96%