Symmetric sequence subspaces of C(α), II

Abstract

If α is an ordinal, then the space of all ordinals less than or equal to α is a compact Hausdorff space when endowed with the order topology. Let C(α) be the space of all continuous real-valued functions defined on the ordinal interval [0, α]. We characterize the symmetric sequence spaces which embed into C(α) for some countable ordinal α. A hierarchy (Eα) of symmetric sequence spaces is constructed so that, for each countable ordinal α, Eα embeds into C(ωωα), but does not embed into C(ωωβ) for any β < α.