A choice-free proof of Mal'cev's theorem on quasivarieties
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908548556914688 |
|---|---|
| author | Shen, Guozhen |
| author_facet | Shen, Guozhen |
| contents | In 1966, Mal'cev proved that a class $\mathcal{K}$ of first-order structures with a specified signature is a quasivariety if and only if $\mathcal{K}$ contains a unit and is closed under isomorphisms, substructures, and reduced products. In this article, we present a proof of this theorem in $\mathsf{ZF}$ (the Zermelo--Fraenkel set theory without the axiom of choice). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A choice-free proof of Mal'cev's theorem on quasivarieties Shen, Guozhen Logic Primary 08C15, Secondary 03C05, 03E25 In 1966, Mal'cev proved that a class $\mathcal{K}$ of first-order structures with a specified signature is a quasivariety if and only if $\mathcal{K}$ contains a unit and is closed under isomorphisms, substructures, and reduced products. In this article, we present a proof of this theorem in $\mathsf{ZF}$ (the Zermelo--Fraenkel set theory without the axiom of choice). |
| title | A choice-free proof of Mal'cev's theorem on quasivarieties |
| topic | Logic Primary 08C15, Secondary 03C05, 03E25 |
| url | https://arxiv.org/abs/2501.00766 |