κ -Ohio completeness

Abstract

Generalizing the Ohio completeness property, we introduce the notion of $\kappa$-Ohio completeness. Although many results from a previous paper by the authors may easily be adapted for this new property, there are also some interesting differences. We provide several examples to illustrate this. We also have a consistency result; depending on the value of the cardinal $\mathfrak{d}$, the countable union of open and ${\omega }_1$-Ohio complete subspaces may or may not be ${\omega }_1$-Ohio complete.