Continuum Many Different Things: Localisation, Anti-Localisation and Yorioka Ideals

Cardona, Miguel A.; Klausner, Lukas Daniel; Mejía, Diego

doi:10.48550/arxiv.2110.11614

Cited by 1 publication

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [KM21] it is shown that there exists a model in which there are uncountably many mutually different cardinals of the form d b,h ω ( ✟ ✟ ∋ ∞ ). In fact, with a little bit more work, Cardona, Klausner & Mejía showed in [CKM21] that there exists a model in which there are 2 ℵ 0 many mutually different cardinals of each of the forms…”

Section: Separating Cardinals Of the Form Dmentioning

confidence: 99%

“…Such cardinals were first studied by Goldstern & Shelah [GS93]. Later, a connection between these cardinals, Yorioka ideals and the strong measure zero ideal was given by Osuga & Kamo [KO08,KO14] and it was shown recently by Cardona, Klausner & Mejía [CKM21] that there can be models with 2 ℵ 0 many (b, h)-localisation numbers with mutually distinct cardinality.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Separating Many Localisation Cardinals on the Generalised Baire Space

VLUGT

2023

J. symb. log.

View full text Add to dashboard Cite

Given a cofinal cardinal function $h\in {}^{\kappa }\kappa $ for $\kappa $ inaccessible, we consider the dominating h-localisation number, that is, the least cardinality of a dominating set of h-slaloms such that every $\kappa $ -real is localised by a slalom in the dominating set. It was proved in [3] that the dominating localisation numbers can be consistently different for two functions h (the identity function and the power function). We will construct a $\kappa ^+$ -sized family of functions h and their corresponding localisation numbers, and use a ${\leq }\kappa $ -supported product of a cofinality-preserving forcing to prove that any simultaneous assignment of these localisation numbers to cardinals above $\kappa $ is consistent. This answers an open question from [3].

show abstract

Section: Separating Cardinals Of the Form Dmentioning

confidence: 99%

mentioning

confidence: 99%