On the minimal cover property and certain notions of finite
From MaRDI portal
Publication:1661686
DOI10.1007/s00153-017-0595-yzbMath1446.03083OpenAlexW2769845943MaRDI QIDQ1661686
Publication date: 16 August 2018
Published in: Archive for Mathematical Logic (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00153-017-0595-y
partially ordered setsaxiom of choicelinearly ordered setscompact spaceweak axioms of choicenotions of finiteminimal cover propertyFraenkel-Mostowski modelPincus Transfer Theorem
Partial orders, general (06A06) Combinatorics of partially ordered sets (06A07) Compactness (54D30) Consistency and independence results (03E35) Total orders (06A05) Axiom of choice and related propositions (03E25)
Related Items
MA(ℵ0) restricted to complete Boolean algebras and choice ⋮ Łoś's theorem and the axiom of choice ⋮ Maximal independent sets, variants of chain/antichain principle and cofinal subsets without AC ⋮ Some independence results about compact metrizable spaces and two notions of finiteness ⋮ On a theorem of Kurepa for partially ordered sets and weak choice ⋮ On the interrelation of a theorem of Juhász and certain weak axioms of choice
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The strength of the \(\Delta\)-system lemma
- The structure of amorphous sets
- Well ordered subsets of linearly ordered sets
- On the minimal cover property in \(\mathbf{ZF}\)
- ON RAMSEY’S THEOREM AND THE EXISTENCE OF INFINITE CHAINS OR INFINITE ANTI-CHAINS IN INFINITE POSETS
- On the set-theoretic strength of the existence of disjoint cofinal sets in posets without maximal elements
- The independence of various definitions of finiteness
- On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice
- Definitions of finite
- Dependences between definitions of finiteness
- Classes of Dedekind finite cardinals
- Adding dependent choice
- Ramsey's theorem in the hierarchy of choice principles
- Finiteness and choice
- Axioms of multiple choice
- Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods
- The axiom of choice