Abstract
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or antichains. This allows us to prove some consequences of the Boolean Prime Ideal theorem using arguments in the style of those that use Zorn’s Lemma or Martin’s Axiom.
Original language | English |
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Pages (from-to) | 25-38 |
Number of pages | 14 |
Journal | Fundamenta Mathematicae |
Volume | 245 |
Issue number | 1 |
DOIs | |
State | Published - 2019 |
Externally published | Yes |
Keywords
- Axiom of Choice
- Boolean Prime Ideal theorem
- Forcing axiom
- Forcing notion
- Generic filter
- Weak choice principles
- Zorn’s Lemma