Add to ORKGChain conditions are one of the major tools used in the theory of forcing. We say that a partial order has the countable chain condition if every antichain (in the sense of forcing) is countable. Without the axiom of choice antichains tend to be of little use, for various reasons, and in this short note we study a number of conditions which in ZFC are equivalent to the countable chain condition.Comment: 15 pages; removed problematic proof and added new result
Abstract. Rationals and countable ordinals are important examples of structures with decidable monad...
Defant, Engen, and Miller defined a permutation to be uniquely sorted if ithas exactly one preimage ...
AbstractCircumstances in which the countable chain condition implies separability are investigated. ...
summary:In set theory without the axiom of choice (AC), we observe new relations of the following st...
AbstractThe special role of countability in topology has been recognized and commented upon very ear...
Abstract. Let the chain antichain principle (CAC) be the statement that each partial order on N poss...
Abstract. A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chain-complete partial...
1. Every anti-chain in P has cardinality 1 =) every anti-chain in F has cardinality 1 2. There exist...
The well-quasi-ordering (i.e., a well-founded quasi-ordering such that allantichains are finite) tha...
In extremal set theory our usual goal is to find the maximal size of a family of subsets of an $n$-e...
We study selective and game-theoretic versions of properties like the ccc, weak Lindelöfness and sep...
We have observations concerning the set theoretic strength of the following combinatorial statements...
A class of finite tournaments determined by a set of "forbidden subtournaments" is wellqua...
We show that Morley's theorem on the number of countable models of a countable first-order theory be...
In set theory without the Axiom of Choice (AC), we observe new relations of the following statements...
Abstract. Rationals and countable ordinals are important examples of structures with decidable monad...
Defant, Engen, and Miller defined a permutation to be uniquely sorted if ithas exactly one preimage ...
AbstractCircumstances in which the countable chain condition implies separability are investigated. ...
summary:In set theory without the axiom of choice (AC), we observe new relations of the following st...
AbstractThe special role of countability in topology has been recognized and commented upon very ear...
Abstract. Let the chain antichain principle (CAC) be the statement that each partial order on N poss...
Abstract. A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chain-complete partial...
1. Every anti-chain in P has cardinality 1 =) every anti-chain in F has cardinality 1 2. There exist...
The well-quasi-ordering (i.e., a well-founded quasi-ordering such that allantichains are finite) tha...
In extremal set theory our usual goal is to find the maximal size of a family of subsets of an $n$-e...
We study selective and game-theoretic versions of properties like the ccc, weak Lindelöfness and sep...
We have observations concerning the set theoretic strength of the following combinatorial statements...
A class of finite tournaments determined by a set of "forbidden subtournaments" is wellqua...
We show that Morley's theorem on the number of countable models of a countable first-order theory be...
In set theory without the Axiom of Choice (AC), we observe new relations of the following statements...
Abstract. Rationals and countable ordinals are important examples of structures with decidable monad...
Defant, Engen, and Miller defined a permutation to be uniquely sorted if ithas exactly one preimage ...
AbstractCircumstances in which the countable chain condition implies separability are investigated. ...