Cardinal characteristics on bounded generalised Baire spaces

Abstract

We will give an overview of four families of cardinal characteristics defined on subspaces ${\prod }_{\alpha \in \kappa }b\left(\alpha \right)$ of the generalised Baire space ${}^{\kappa }\kappa$, where κ is strongly inaccessible and $b\in {}^{\kappa }\kappa$. 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.