Ancestors

Toot

Written by Naïm Camille Favier on 2025-01-28 at 18:01

Wait, Kőnig's lemma is (classically) equivalent to Brouwer's fan theorem (Cantor space is compact)? That explains why you can prove it using Tychonoff's theorem!

(So many names...)

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Descendants

Written by aramya on 2025-01-28 at 18:38

@ncf le théorème du ventilateur

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Written by Naïm Camille Favier on 2025-01-28 at 18:43

@aramya de l'éventail, plutôt :)

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Written by Martin Escardo on 2025-01-28 at 20:48

@ncf

Any classical theorem is classically equivalent to any other classical theorem.

Both Kőnig's lemma and Brouwer's fan theorem hold classically.

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Written by Naïm Camille Favier on 2025-01-28 at 20:54

@MartinEscardo Yeah, ok. I didn't dig too deep but it seems like the relationship between the two is stronger than "they're both classical theorems": one is constructively equivalent to the contrapositive of (a weak version of) the other, or something.

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