Abstract
In the context of ZF, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the AC.
| Translated title of the contribution | El teorema de Hindman en la jerarquía de los principios de elección |
|---|---|
| Original language | English |
| Article number | 2350002 |
| Journal | Journal of Mathematical Logic |
| DOIs | |
| State | Accepted/In press - 2023 |
Keywords
- Fraenkel-Mostowski model
- Hindman's theorem
- Weak choice principles
- choiceless set theory