Relations between some cardinals in the absence of the Axiom of Choice

Details Relations between some cardinals in the absence of the Axiom of Choice Relations between some cardinals in the absence of the Axiom of Choice

2000-10-27

arxiv.org/abs/math/0010268v1

Mathematics

Logic

Scientific paper

If we assume the axiom of choice, then every two cardinal numbers are comparable. In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using the axiom of choice.

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