A consistency result on long cardinal sequences

For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$it is consistent that $2^{\kappa}$ is as large as you wish, and every function $f: \eta \longrightarrow\left[\kappa, 2^{\kappa}\right] \cap$ Card with $f(\alpha)=\kappa$ for $c f(\alpha)<\kappa$ is the cardinal sequence of some lo...

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Detalhes bibliográficos
Autores: Martínez Alonso, Juan Carlos, Soukup, Lajos
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2021
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositório:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/185509
Acesso em linha:https://hdl.handle.net/2445/185509
Access Level:Acceso aberto
Palavra-chave:Topologia
Àlgebra de Boole
Teoria de conjunts
Topology
Boolean algebras
Set theory
Descrição
Resumo:For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$it is consistent that $2^{\kappa}$ is as large as you wish, and every function $f: \eta \longrightarrow\left[\kappa, 2^{\kappa}\right] \cap$ Card with $f(\alpha)=\kappa$ for $c f(\alpha)<\kappa$ is the cardinal sequence of some locally compact scattered space.