Szlenk and w-dentability indices of the Banach spaces C([0,α])

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Let α be an infinite ordinal and γ the unique ordinal satisfying ωωγ≤ α< ωωγ⁺¹. We show that the Banach space C([0,α]) of all continuous scalar-valued functions on the compact ordinal interval [0,α] has Szlenk index equal to ωγ⁺¹ and w-dentability index equal to ω¹⁺γ⁺¹.