Title:	Embeddability Between Orderings and GCH
Authors:	Freire, Rodrigo de Alvarenga
Assunto::	Hipótese contínua Estrutura de ordenamentos lineares Relações de partição
Issue Date:	10-Nov-2021
Publisher:	Theoretical Computer Science Department, Jagiellonian University, Poland
Citation:	FREIRE, Rodrigo A. Embeddability Between Orderings and GCH. Reports on Mathematical Logic, Kraków, n. 56, p. 101-109, 2021. DOI: https://doi.org/10.4467/20842589RM.21.005.14377. Disponível em: https://www.ejournals.eu/rml/2021/Number-56/art/20102/. Acesso em: 06 jan. 2021.
Abstract:	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.
Licença::	"Copyrights and sharing The articles published after 2017 in Reports on Mathematical Logic are available under a licence Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). For aricles till 2017 your use is permitted by an applicable exception or limitation – see: Ustawa z dnia 4 lutego 1994 r. o prawie autorskim i prawach pokrewnych Read more about the license CC BY-NC-ND 4.0: https://creativecommons.org/licenses/by-nc-nd/4.0/ View Legal Code: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode. Fonte: https://www.ejournals.eu/rml/menu/982/. Acesso em: 06 jan. 2022.
DOI:	https://doi.org/10.4467/20842589RM.21.005.14377
Appears in Collections:	Artigos publicados em periódicos e afins

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