Embeddability Between Orderings and GCH
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| Main Author: | |
|---|---|
| Publication Date: | 2021 |
| Format: | Article |
| Language: | eng |
| Source: | Repositório Institucional da UnB |
| Download full: | https://repositorio.unb.br/handle/10482/42677 https://doi.org/10.4467/20842589RM.21.005.14377 |
Summary: | 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. |
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