1
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...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Text |
| Language: | English |
| Published: |
2008
|
| Subjects: | |
| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.7417 http://arxiv.org/pdf/math/9712274v1.pdf |
| Summary: | 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 |
|---|