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Archive for Mathematical Logic

, Volume 57, Issue 5–6, pp 665–686 | Cite as

On the minimal cover property and certain notions of finite

  • Eleftherios TachtsisEmail author
Article

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.

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 

Mathematics Subject Classification

Primary 03E25 Secondary 03E35 06A05 06A06 06A07 54D30 

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the AegeanKarlovassi, SamosGreece

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