Generic dichotomy for homomorphisms for $E_0^\mathbb{N}$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929446920912896 |
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| author | Shani, Assaf |
| author_facet | Shani, Assaf |
| contents | We prove the following dichotomy. Given an analytic equivalence relation $E$, either ${E_0^{\mathbb{N}}}\leq_B{E}$ or else any Borel homomorphism from $E_0^{\mathbb{N}}$ to $E$ is "very far from a reduction", specifically, it factors, on a comeager set, through the projection map $(2^{\mathbb{N}})^{\mathbb{N}}\to (2^{\mathbb{N}})^k$ for some $k\in\mathbb{N}$. As a corollary, we prove that $E_0^{\mathbb{N}}$ is a prime equivalence relation, answering a question on Clemens. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generic dichotomy for homomorphisms for $E_0^\mathbb{N}$ Shani, Assaf Logic 03E15, 54H05 We prove the following dichotomy. Given an analytic equivalence relation $E$, either ${E_0^{\mathbb{N}}}\leq_B{E}$ or else any Borel homomorphism from $E_0^{\mathbb{N}}$ to $E$ is "very far from a reduction", specifically, it factors, on a comeager set, through the projection map $(2^{\mathbb{N}})^{\mathbb{N}}\to (2^{\mathbb{N}})^k$ for some $k\in\mathbb{N}$. As a corollary, we prove that $E_0^{\mathbb{N}}$ is a prime equivalence relation, answering a question on Clemens. |
| title | Generic dichotomy for homomorphisms for $E_0^\mathbb{N}$ |
| topic | Logic 03E15, 54H05 |
| url | https://arxiv.org/abs/2408.01261 |