Cantor-Bernstein implies Excluded Middle
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We prove in constructive logic that the statement of the Cantor-Bernstein theorem implies excluded middle. This establishes that the Cantor-Bernstein theorem can only be proven assuming the full power of classical logic. The key ingredient is a theorem of Martín Escardó stating that quantification over a particular subset of the Cantor space 2^N, the so-called one-point compactification of N, preserves decidable predicates.
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