Egorov ideals

Abstract

We study Egorov ideals, that is ideals on $\omega$ for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological $\bf{\Sigma^0_2}$ ideal is Egorov if and only if it is countably generated. In particular, up to isomorphism, there are only three non-pathological $\bf{\Sigma^0_2}$ Egorov ideals. On the other hand, we construct $2^\omega$ pairwise non-isomorphic Borel Egorov ideals. Moreover, we characterize when a product of ideals is Egorov.