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Jul 28, 2023 at 8:38 comment added Milo Moses @JoelDavidHamkins I agree, I don't think that Freedman's conjecture is correct - despite how pleasing his topological heuristics he presents are.
Jul 27, 2023 at 13:53 comment added Joel David Hamkins But also, that conjecture seems to be refuted by David's answer above, which shows that a certain nonzero constant proportion of the sentences are provable, so it can't be less than the square root in the limit.
Jul 27, 2023 at 12:17 comment added Joel David Hamkins Pure alphabetical order will not usually have order type $\mathbb{Z}^+$. For example, see my essay infinitelymore.xyz/p/the-book-of-numbers for an analysis and discussion of the numbers in alphabetical order, which have order type $\mathbb{N}\cdot(1+\mathbb{Q})+1$.
Jul 27, 2023 at 11:59 history answered Milo Moses CC BY-SA 4.0