A constructive Knaster-Tarski proof of the uncountability of the reals

2019/02/20 by Ingo Blechschmidt, Blechschmidt, Ingo, Matthias Hutzler +1 · 1 voice
Computer Science · Mathematics · Psychology · #03F99 #26E40 #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Overview (math.HO) #Logic (math.LO) #Mathematical and Theoretical Analysis #Philosophy and Theoretical Science #math.HO #math.LO

paper · pdf · doi:10.48550/arxiv.1902.07366

openalex publication_date 2019/02/20 · arxiv published 2019/02/20 · arxiv updated 2019/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an uncountability proof of the reals which relies on their order completeness instead of their sequential completeness. We use neither a form of the axiom of choice nor the law of excluded middle, therefore the proof applies to the MacNeille reals in any flavor of constructive mathematics. The proof leans heavily on Levy's unusual proof of the uncountability of the reals.

Citations

• An Unusual Proof that the Reals are Uncountable

Discussions

• And see arxiv.org/abs/1902.07366 for a third different proof. [bsky, 2 points, 0 comments]

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