Ideals generated by families of sequences of natural numbers

Pratulananda Das, Szymon Głcab, Rafał Filipów, Jacek Tryba

Published 2020-11-07Version 1

We consider ideals on $\omega\times\omega$ generated by subsets of $\omega^\omega$. Namely, for $\mathcal{F}\subset \omega^\omega$ we define $$\mathcal{I}(\mathcal{F})=\{A\subset \omega\times\omega:\exists f\in \mathcal{F}\,\forall^\infty n\in\omega\, (|\{k:(n,k)\in A\}|\leq f(n))\}.$$ These ideals encompass other well known ideals e.g.~$fin\times fin$ and $ED$. We examine some properties of these ideals including topological complexity and cardinal characteristics associated with them.