Consider the subset A of (ℤ+)ω consisting of all infinite sequences of positive integers x = (x1, x2, …) that end in an infinite string of I’s. Give A the following order: x<y if xn<yn and xi = yj for i > n. We call this the “antidictionary order” on A.
(a) Show that for every n, there is a section of A that has the same order type as (ℤ+)n in the dictionary order.
(b) Show A is well-ordered.
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