Embeddability Between Orderings and GCH

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,...

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Bibliographic Details
Published inReports on mathematical logic Vol. 56; no. 56; pp. 101 - 109
Main Author Freire, Rodrigo A
Format Journal Article
LanguageEnglish
Published Kraków Wydawnictwo Uniwersytetu Jagiellońskiego 2021
Jagiellonian University Press
Jagiellonian University-Jagiellonian University Press
Subjects
Equivalence
Logic
structure of linear orderings
continuum hypothesis
partition relations
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0137-2904
2084-2589
DOI:10.4467/20842589RM.21.005.14377