Surjections from ℕ onto ℝ. Surjections from S ⊂ ℕ onto ℕ^ℕ. All that.
Channel: Nikolaj-K
Date: 2024-04-07

For a helpful constructive logic basics video with upshots, by me from last year, see https://youtu.be/-lPrjPHElik
For a related and relevant discussion on computably enumerable sets and their compliments, see this 4yo video https://youtu.be/Ox0tD58DTG0
For some of the non-theorems in the list it helps to understand \Pi_0^2-complete sets.
The references video on how the Axiom of Choice and Regularity each imply LEM is at https://youtu.be/2EOW23uVcRA

Keywords:
https://en.wikipedia.org/wiki/Subcountability
https://en.wikipedia.org/wiki/Effective_topos

Previous ℕ^ℕ into ℕ paper: https://math.andrej.com/wp-content/uploads/2011/06/injection.pdf
April ℕ onto ℝ paper: https://arxiv.org/abs/2404.01256
2022 talk on the latter: https://www.youtube.com/live/4CBFUojXoq4

Shownotes presented
https://gist.github.com/Nikolaj-K/470eaf79d3289dd942e2ba128ff04f13