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uncountable subset family, pairwise intersections are finite

Source: VJIMC 2000 1.1

July 26, 2021
set theorySetsinfinitycollege contestsreal analysis

Problem Statement

Is there a countable set YY and an uncountable family F\mathcal F of its subsets such that for every two distinct A,B∈FA,B\in\mathcal F, their intersection A∩BA\cap B is finite?
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