Sparse graphs and the fixed points on type spaces property
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910564057350144 |
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| author | Sullivan, Rob |
| author_facet | Sullivan, Rob |
| contents | We examine the topological dynamics of the automorphism groups of omega-categorical sparse graphs resulting from Hrushovski constructions. Specifically, we consider the fixed points on type spaces property, which a structure M has if, for each positive integer n, every Aut(M)-subflow of the space of n-types has a fixed point. Extending a result of Evans, Hubicka and Nesetril, we show that there exists an omega-categorical structure M, resulting from a Hrushovski construction, such that no omega-categorical expansion of M has the fixed points on type spaces property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06829 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sparse graphs and the fixed points on type spaces property Sullivan, Rob Logic 03C15, 37B05, 20B27, 05C55, 05D10 We examine the topological dynamics of the automorphism groups of omega-categorical sparse graphs resulting from Hrushovski constructions. Specifically, we consider the fixed points on type spaces property, which a structure M has if, for each positive integer n, every Aut(M)-subflow of the space of n-types has a fixed point. Extending a result of Evans, Hubicka and Nesetril, we show that there exists an omega-categorical structure M, resulting from a Hrushovski construction, such that no omega-categorical expansion of M has the fixed points on type spaces property. |
| title | Sparse graphs and the fixed points on type spaces property |
| topic | Logic 03C15, 37B05, 20B27, 05C55, 05D10 |
| url | https://arxiv.org/abs/2309.06829 |