Special subsets of the generalized Cantor space and generalized Baire space

Mathematical Logic Quarterly 66 (4):418-437 (2020)
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Abstract

In this paper, we are interested in parallels to the classical notions of special subsets in defined in the generalized Cantor and Baire spaces (2κ and ). We consider generalizations of the well‐known classes of special subsets, like Lusin sets, strongly null sets, concentrated sets, perfectly meagre sets, σ‐sets, γ‐sets, sets with the Menger, the Rothberger, or the Hurewicz property, but also of some less‐know classes like X‐small sets, meagre additive sets, Ramsey null sets, Marczewski, Silver, Miller, and Laver‐null sets. We notice that many classical theorems regarding these classes can be relatively easy generalized to higher cardinals although sometimes with some additional assumptions. This paper serves as a catalogue of such results along with some other generalizations and open problems.

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References found in this work

Set Theory.T. Jech - 2005 - Bulletin of Symbolic Logic 11 (2):243-245.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Regularity properties on the generalized reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
Generalized Silver and Miller measurability.Giorgio Laguzzi - 2015 - Mathematical Logic Quarterly 61 (1-2):91-102.

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