Model Theory of Hilbert Spaces with a Discrete Group Action
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909742231715840 |
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| author | Berenstein, Alexander Pérez, Juan Manuel |
| author_facet | Berenstein, Alexander Pérez, Juan Manuel |
| contents | In this paper we study expansions of infinite dimensional Hilbert spaces with a unitary representation of a discrete countable group. When the group is finite, we prove the theory of the corresponding expansion, regardless if it is existentially closed, has quantifier elimination, is $\aleph_0$-categorical, $\aleph_0$-stable and SFB. On the other hand, when the group involved is countably infinite, the theory of the Hilbert space expanded by the representation of this group is $\aleph_0$-categorical up to perturbations. Additionally, when the expansion is model complete, we prove that it is $\aleph_0$-stable up to perturbations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Model Theory of Hilbert Spaces with a Discrete Group Action Berenstein, Alexander Pérez, Juan Manuel Logic In this paper we study expansions of infinite dimensional Hilbert spaces with a unitary representation of a discrete countable group. When the group is finite, we prove the theory of the corresponding expansion, regardless if it is existentially closed, has quantifier elimination, is $\aleph_0$-categorical, $\aleph_0$-stable and SFB. On the other hand, when the group involved is countably infinite, the theory of the Hilbert space expanded by the representation of this group is $\aleph_0$-categorical up to perturbations. Additionally, when the expansion is model complete, we prove that it is $\aleph_0$-stable up to perturbations. |
| title | Model Theory of Hilbert Spaces with a Discrete Group Action |
| topic | Logic |
| url | https://arxiv.org/abs/2409.03923 |