Abstract
In set theory without the axiom of choice, we investigate the deductive strength of the principle “every topological space with the minimal cover property is compact”, and its relationship with certain notions of finite as well as with properties of linearly ordered sets and partially ordered sets.
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Tachtsis, E. On the minimal cover property and certain notions of finite. Arch. Math. Logic 57, 665–686 (2018). https://doi.org/10.1007/s00153-017-0595-y
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DOI: https://doi.org/10.1007/s00153-017-0595-y
Keywords
- Axiom of choice
- Weak axioms of choice
- Minimal cover property
- Compact space
- Notions of finite
- Partially ordered set
- Linearly ordered set
- Cofinal well-founded subset of a partially ordered set
- Chain and antichain in a partially ordered set
- Fraenkel–Mostowski (FM) permutation models of ZFA + ¬AC
- Pincus’ transfer theorems