Open AccessEmbeddability Between Orderings and GCH
Author(s) -
Rodrigo Argenton Freire
Publication year - 2021
Publication title -
reports on mathematical logic
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.101
H-Index - 6
eISSN - 2084-2589
pISSN - 0137-2904
DOI - 10.4467/20842589rm.21.005.14377
Subject(s) - mathematics , converse , exponentiation , discrete mathematics , pure mathematics , combinatorics , mathematical analysis , geometry
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 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.