Cardinal characteristics on bounded generalised Baire spaces

We will give an overview of four families of cardinal characteristics defined on subspaces ∏ α ∈ κ b ( α ) of the generalised Baire space κ κ , where κ is strongly inaccessible and b ∈ κ κ . The considered families are bounded versions of the dominating, eventual difference, localisation and antilocalisation numbers, and their dual cardinals. We investigate parameters for which these cardinals are nontrivial and how the cardinals relate to each other and to other cardinals of the generalised Cichoń diagram. Finally we prove that different choices of parameters may lead to consistently distinct cardinals.

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Publication Details

Journal
Annals of Pure and Applied Logic
Published
2025-03-12
DOI
https://doi.org/10.1016/j.apal.2025.103582
Primary Topic
Advanced Topology and Set Theory
Type
article
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article

Cardinal characteristics on bounded generalised Baire spaces

Tristan van der Vlugt
Annals of Pure and Applied Logic
Advanced Topology and Set Theory
article

Cardinal characteristics on bounded generalised Baire spaces

Tristan van der Vlugt
article en

Abstract

We will give an overview of four families of cardinal characteristics defined on subspaces ∏ α ∈ κ b ( α ) of the generalised Baire space κ κ , where κ is strongly inaccessible and b ∈ κ κ . The considered families are bounded versions of the dominating, eventual difference, localisation and antilocalisation numbers, and their dual cardinals. We investigate parameters for which these cardinals are nontrivial and how the cardinals relate to each other and to other cardinals of the generalised Cichoń diagram. Finally we prove that different choices of parameters may lead to consistently distinct cardinals.

Annals of Pure and Applied LogicVol. 176(7)
Universität Hamburg (DE)
Reduced inequalities
Openalex Percentile: Top 91%
Advanced Topology and Set Theory
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