Abstract

We study Egorov ideals, that is ideals on ω for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological Σ20 ideal is Egorov if and only if it is countably generated. In particular, up to isomorphism, there are only three non-pathological Σ20 Egorov ideals. On the other hand, we construct 2ω pairwise non-isomorphic Borel Egorov ideals. Moreover, we characterize when a product of ideals is Egorov.

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