Symmetric Sequence Subspaces of C({alpha})

Two main results are shown: (1) a characterisation of the symmetricsequence spaces which embed into C(), and (2) a characterisation,in terms of the Orlicz function M, of the Orlicz sequence spacesh_M which embed into C(K) for some countable compact Hausdorffspace K. The proofs make use of the Schreier families of sets,which have found wide applications in Banach space theory.