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$\omega_1$-strongly compact cardinals and normality
Identificadores del recurso
0166-8641
http://hdl.handle.net/2445/214429
744329
Origin
(Dipòsit Digital de la Universitat de Barcelona)

File

Title:
$\omega_1$-strongly compact cardinals and normality
Tema:
Espais topològics
Topologia
Teoria de conjunts
Nombres cardinals
Topological spaces
Topology
Set theory
Cardinal numbers
Description:
We present more applications of the recently introduced -strongly compact cardinals in the context of either consistency or reflection results in General Topology, focusing on issues related to normality. In particular, we show that such large cardinal notion provides a new upper bound for the consistency strength of the statement “All normal Moore spaces are metrizable” (NMSC). The proof uses random forcing, as in the original consistency proof of NMSC due to Nykos-Kunen-Solovay (see Fleissner [10]). We establish a compactness theorem for normality (i.e., reflection of non-normality) in the realm of first countable spaces, using the least -strongly compact cardinal, as well as two more similar compactness results on related topological properties. We finish the paper by combining the techniques of reflection and forcing to show that our new upper bound for the consistency strength of NMSC can be also obtained via Cohen forcing, using some arguments from Dow-Tall-Weiss.
Source:
Articles publicats en revistes (Matemàtiques i Informàtica)
Idioma:
English
Relation:
Reproducció del document publicat a: https://doi.org/10.1016/j.topol.2022.108276
Topology and its Applications, 2023, vol. 323
https://doi.org/10.1016/j.topol.2022.108276
Autor/Productor:
Bagaria, Joan
da Silva, Samuel G.
Publisher:
Elsevier B.V.
Rights:
cc-by-nc-nd (c) Joan Bagaria et al., 2023
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
Date:
2024-07-08T11:23:53Z
2023-01-01
2024-07-08T11:23:59Z
Tipo de recurso:
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Format:
23 p.
application/pdf

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    1. <dc:title>$\omega_1$-strongly compact cardinals and normality</dc:title>

    2. <dc:creator>Bagaria, Joan</dc:creator>

    3. <dc:creator>da Silva, Samuel G.</dc:creator>

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    6. <dc:subject.classification>Teoria de conjunts</dc:subject.classification>

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    12. <dcterms:abstract>We present more applications of the recently introduced -strongly compact cardinals in the context of either consistency or reflection results in General Topology, focusing on issues related to normality. In particular, we show that such large cardinal notion provides a new upper bound for the consistency strength of the statement “All normal Moore spaces are metrizable” (NMSC). The proof uses random forcing, as in the original consistency proof of NMSC due to Nykos-Kunen-Solovay (see Fleissner [10]). We establish a compactness theorem for normality (i.e., reflection of non-normality) in the realm of first countable spaces, using the least -strongly compact cardinal, as well as two more similar compactness results on related topological properties. We finish the paper by combining the techniques of reflection and forcing to show that our new upper bound for the consistency strength of NMSC can be also obtained via Cohen forcing, using some arguments from Dow-Tall-Weiss.</dcterms:abstract>

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    24. <dc:relation>Reproducció del document publicat a: https://doi.org/10.1016/j.topol.2022.108276</dc:relation>

    25. <dc:relation>Topology and its Applications, 2023, vol. 323</dc:relation>

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