 Solution

ID: past-exam-of-the-logic-and-set-theory-course-of-the-university-of-oxford/2008/b/7/2/solution

S \subseteq ω

1_{S} : ω \to {0, 1}

u

{n \in ω : u (n) = 1}

. These maps are mutually inverse, so

∣^{ω} 2∣ = ∣ P (ω) ∣ = 2^{ℵ_{0}} .

Here the left superscript denotes the set of functions from

ω

into

2

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