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In rough historical these are the groups for which we know the topological Vaught conjecture: 0.1 Theorem (Folklore) All locally compact Polish groups satisfy Vaught’s conjecture – that is to say, if G is a locally compact Polish group acting continuously on a Polish space X then either |X/G | ≤ ℵ0...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.239.7417 2023-05-15T18:11:54+02:00 1 Greg Hjorth The Pennsylvania State University CiteSeerX Archives 2008 application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.7417 http://arxiv.org/pdf/math/9712274v1.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.7417 http://arxiv.org/pdf/math/9712274v1.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://arxiv.org/pdf/math/9712274v1.pdf text 2008 ftciteseerx 2016-01-07T19:06:19Z In rough historical these are the groups for which we know the topological Vaught conjecture: 0.1 Theorem (Folklore) All locally compact Polish groups satisfy Vaught’s conjecture – that is to say, if G is a locally compact Polish group acting continuously on a Polish space X then either |X/G | ≤ ℵ0 or there is a perfect set of points with different orbits (and hence |X/G | ≥ 2 ℵ0 0.2 Theorem (Sami) Abelian Polish groups satisfy Vaught’s conjecture. 0.3 Theorem (Hjorth-Solecki) Invariantly metrizable and nilpotent Polish groups satisfy Vaught’s conjecture. 0.4 Theorem (Becker) Complete left invariant metric and solvable Polish groups satisfy Vaught’s conjecture. In each of these case the result was shortly or immediately after extended to analytic sets. For this purpose let us write TVC(G, Σ 1 Text sami Unknown |
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English |
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In rough historical these are the groups for which we know the topological Vaught conjecture: 0.1 Theorem (Folklore) All locally compact Polish groups satisfy Vaught’s conjecture – that is to say, if G is a locally compact Polish group acting continuously on a Polish space X then either |X/G | ≤ ℵ0 or there is a perfect set of points with different orbits (and hence |X/G | ≥ 2 ℵ0 0.2 Theorem (Sami) Abelian Polish groups satisfy Vaught’s conjecture. 0.3 Theorem (Hjorth-Solecki) Invariantly metrizable and nilpotent Polish groups satisfy Vaught’s conjecture. 0.4 Theorem (Becker) Complete left invariant metric and solvable Polish groups satisfy Vaught’s conjecture. In each of these case the result was shortly or immediately after extended to analytic sets. For this purpose let us write TVC(G, Σ 1 |
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Greg Hjorth |
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2008 |
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.7417 http://arxiv.org/pdf/math/9712274v1.pdf |
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