The structure of [Formula: see text] -maximal cofinitary groups

We study [Formula: see text] -maximal cofinitary groups for [Formula: see text] regular uncountable, [Formula: see text] 1. Any [Formula: see text] -maximal cofinitary group has [Formula: see text] many orbits under the natural group action of [Formula: see text] on [Formula: see text] . 2. If [Form...

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Detalles Bibliográficos
Autores principales: Fischer, Vera, Switzer, Corey Bacal
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10227154/
https://www.ncbi.nlm.nih.gov/pubmed/37260527
http://dx.doi.org/10.1007/s00153-022-00859-x
Descripción
Sumario:We study [Formula: see text] -maximal cofinitary groups for [Formula: see text] regular uncountable, [Formula: see text] 1. Any [Formula: see text] -maximal cofinitary group has [Formula: see text] many orbits under the natural group action of [Formula: see text] on [Formula: see text] . 2. If [Formula: see text] then any partition of [Formula: see text] into less than [Formula: see text] many sets can be realized as the orbits of a [Formula: see text] -maximal cofinitary group. 3. For any regular [Formula: see text] it is consistent that there is a [Formula: see text] -maximal cofinitary group which is universal for groups of size [Formula: see text] . If we only require the group to be universal for groups of size [Formula: see text] then this follows from [Formula: see text] . .

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