The sole purpose of this paper is to give an algebraic characterization, in terms of a superamalgamation property, of a local version of Craig interpolation theorem that has been introduced and studied in earlier papers. We continue ongoing research in abstract algebraic logic and use the framework developed by Andréka– Németi and Sain.
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 ordered set...
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