Embeddability Between Orderings and GCH - Freire, Rodrigo de Alvarenga (2021)
We provide some statements equivalent in ZF C to GCH, and also to GCH above a given cardinal. These statements express the validity of the notions of replete and well-replete car dinals, 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.