Ellis enveloping semigroups in real closed fields
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913195258544128 |
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| author | Baro, Elías Palacín, Daniel |
| author_facet | Baro, Elías Palacín, Daniel |
| contents | We introduce the Boolean algebra of d-semialgebraic (more generally, d-definable) sets and prove that its Stone space is naturally isomorphic to the Ellis enveloping semigroup of the Stone space of the Boolean algebra of semialgebraic (definable) sets. For definably connected o-minimal groups, we prove that this family agrees with the one of externally definable sets in the one-dimensional case. Nonetheless, we prove that in general these two families differ, even in the semialgebraic case over the real algebraic numbers. On the other hand, in the semialgebraic case we characterise real semialgrebraic functions representing Boolean combinations of d-semialgebraic sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07294 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ellis enveloping semigroups in real closed fields Baro, Elías Palacín, Daniel Logic Algebraic Geometry 14P10, 03C45, 03C64, 37B05 We introduce the Boolean algebra of d-semialgebraic (more generally, d-definable) sets and prove that its Stone space is naturally isomorphic to the Ellis enveloping semigroup of the Stone space of the Boolean algebra of semialgebraic (definable) sets. For definably connected o-minimal groups, we prove that this family agrees with the one of externally definable sets in the one-dimensional case. Nonetheless, we prove that in general these two families differ, even in the semialgebraic case over the real algebraic numbers. On the other hand, in the semialgebraic case we characterise real semialgrebraic functions representing Boolean combinations of d-semialgebraic sets. |
| title | Ellis enveloping semigroups in real closed fields |
| topic | Logic Algebraic Geometry 14P10, 03C45, 03C64, 37B05 |
| url | https://arxiv.org/abs/2307.07294 |