A note on dual Dedekind finiteness
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911164097626112 |
|---|---|
| author | Mao, Ruihuan Shen, Guozhen |
| author_facet | Mao, Ruihuan Shen, Guozhen |
| contents | A set $A$ is dually Dedekind finite if every surjection from $A$ onto $A$ is injective; otherwise, $A$ is dually Dedekind infinite. It is proved consistent with $\mathsf{ZF}$ (i.e., the Zermelo--Fraenkel set theory without the axiom of choice) that there exists a family $\langle A_n\rangle_{n\inω}$ of sets such that, for all $n\inω$, $A_n^n$ is dually Dedekind finite whereas $A_n^{n+1}$ is dually Dedekind infinite. This resolves a question that was left open in [J. Truss, Fund. Math. 84, 187--208 (1974)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on dual Dedekind finiteness Mao, Ruihuan Shen, Guozhen Logic Primary 03E35, Secondary 03E10, 03E25 A set $A$ is dually Dedekind finite if every surjection from $A$ onto $A$ is injective; otherwise, $A$ is dually Dedekind infinite. It is proved consistent with $\mathsf{ZF}$ (i.e., the Zermelo--Fraenkel set theory without the axiom of choice) that there exists a family $\langle A_n\rangle_{n\inω}$ of sets such that, for all $n\inω$, $A_n^n$ is dually Dedekind finite whereas $A_n^{n+1}$ is dually Dedekind infinite. This resolves a question that was left open in [J. Truss, Fund. Math. 84, 187--208 (1974)]. |
| title | A note on dual Dedekind finiteness |
| topic | Logic Primary 03E35, Secondary 03E10, 03E25 |
| url | https://arxiv.org/abs/2412.07142 |