Evading predictors with creatures

Abstract:

We continue the theory of evasion and prediction which was introduced by Blass and developed by Brendle, Shelah, and Laflamme. We prove that for arbitrary sufficiently different $f,g\in ^{\omega }\omega$, it is consistent to have ${\mathfrak {e}}_{g}<{\mathfrak {e}}_{f}$, where ${\mathfrak {e}}_{f}$ is the evasion number of the space $\prod _{n<\omega }f(n)$. For this we apply a variant of Shelah’s “creature forcing”.