EMBEDDABILITY BETWEEN ORDERINGS AND THE GCH
REPORTS ON MATHEMATICAL LOGIC(2021)
摘要
We provide some statements equivalent in ZFC to GCH, and also to GCH above a given cardinal. These statements express the validity of the notions of replete and well-replete cardinals, which are introduced and proved to be specially relevant to the study of cardinal exponentiation. As a byproduct, a structure theorem for linear orderings is proved to be equivalent to GCH: for every linear ordering L, at least one of L and its converse is universal for the smaller well-orderings.
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关键词
and phrases, generalized continuum hypothesis, structure of linear orderings, partition relations
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