Chromatic number of the product of graphs, graph homomorphisms, antichains and cofinal subsets of posets without AC
Amitayu Banerjee, Zalán Gyenis (2021)
Commentationes Mathematicae Universitatis Carolinae
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In set theory without the axiom of choice (AC), we observe new relations of the following statements with weak choice principles. If in a partially ordered set, all chains are finite and all antichains are countable, then the set is countable. If in a partially ordered set, all chains are finite and all antichains have size , then the set has size for any regular . Every partially ordered set without a maximal element has two disjoint cofinal sub sets – CS. Every partially...