Imaginaries, products and the adele ring
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910005631909888 |
|---|---|
| author | Derakhshan, Jamshid Hrushovski, Ehud |
| author_facet | Derakhshan, Jamshid Hrushovski, Ehud |
| contents | We describe the imaginary sorts of infinite products in terms of imaginary sorts of the factors. We extend the result to certain reduced powers and then to infinite products $\prod_{i\in I} M_i$ enriched with a predicate for the ideal of finite subsets of $I$. As a special case, using the Hils-Rideau-Kikuchi uniform $p$-adic elimination of imaginaries, we find the imaginary sorts of the ring of rational adeles. Our methods include the use of the Harrington-Kechris-Louveau Glimm-Efros dichotomy both for transitioning from monadic second order imaginaries to first-order reducts, and for proving a certain ``one-way'' model-theoretic orthogonality within the adelic imaginaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_11678 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Imaginaries, products and the adele ring Derakhshan, Jamshid Hrushovski, Ehud Logic 03C95, 03C10 We describe the imaginary sorts of infinite products in terms of imaginary sorts of the factors. We extend the result to certain reduced powers and then to infinite products $\prod_{i\in I} M_i$ enriched with a predicate for the ideal of finite subsets of $I$. As a special case, using the Hils-Rideau-Kikuchi uniform $p$-adic elimination of imaginaries, we find the imaginary sorts of the ring of rational adeles. Our methods include the use of the Harrington-Kechris-Louveau Glimm-Efros dichotomy both for transitioning from monadic second order imaginaries to first-order reducts, and for proving a certain ``one-way'' model-theoretic orthogonality within the adelic imaginaries. |
| title | Imaginaries, products and the adele ring |
| topic | Logic 03C95, 03C10 |
| url | https://arxiv.org/abs/2309.11678 |