53,537
reputation
13
31

Simply Beautiful Art

8/21/2019: I defined a neat ordinal collapsing function:

S(A) ⇔ ∀ f : sup A ↦ sup A, ∃ α ∈ A, ∀ η ∈ α (f(η) ∈ α)

B(α, κ, 0) = κ ∪ {0, K}

B(α, κ, n+1) = {γ + δ | γ, δ ∈ B(α, κ, n)}

             ∪ {Ψ_η(μ) | μ ∈ B(α, κ, n) ∧ η ∈ α ∩ B(α, κ, n)}

B(α, κ) = ⋃ {B(α, κ, n) | n ∈ N}

Ξ(α) = {κ ∈ K′ | κ ∉ B(α, κ) ∧ α ∈ cl(B(α, κ)) ∧ S(⋂ {Ξ(η) ∩ κ | η ∈ B(α, κ) ∩ α})}

Ψ_α = enum(Ξ(α))

where K is a weakly compact cardinal and K' is the (K+1)th hyper-Mahlo or alternatively, the smallest ordinal larger than K closed under γ ↦ M(γ), where M(γ) is the first γ-Mahlo. On its own this doesn't make a notation for large countable ordinals, but it can be used with another ordinal collapsing function for such purpose.

If you need me, you can find me here:

This is the realm of SBA

or on Discord.

My favorite topics include , , , , , and on math.SE.

Some of my favorite posts:

Golf a number bigger than TREE(3)

Largest Number Printable

Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula

How to prove this $\pi$ formula?

Visually stunning math concepts which are easy to explain

25
answers
22
questions
~43k
people reached
  • America
  • Member for 3 years, 11 months
  • 797 profile views
  • Last seen Aug 15 at 12:18

Top tags (51)

Score 137
Posts 43
Posts % 91
Score 43
Posts 4
Score 36
Posts 4
Score 11
Posts 4
Score 7
Posts 3
Score 6
Posts 2

Top posts (47) All Questions Answers | Votes Newest

View all questions and answers

Badges (44)

Gold

Silver

13

Rarest

Bronze

31

Rarest