Talk:Small Veblen ordinal

Link to "Ordinal Analysis"?

I was thinking of adding a link to "Ordinal analysis" in a "See also" section, since this article mentions that the small Veblen ordinal measures the strength of Kruskal's theorem. But since I'm not an expert in this area, I thought I'd float the idea here first in case I'm mistaken about the connection or there are compelling reasons not to make the link. — Preceding unsigned comment added by MisterGoodTime (talk • contribs) 18:07, 20 May 2012 (UTC)

Neither "Kruskal" nor "Veblen" appear to be mentioned in the "Ordinal analysis" article. I think that should be corrected before you do this, else it is not relevant to this article. JRSpriggs (talk) 21:32, 20 May 2012 (UTC)

Unreliable source for "simplification orderings"

On 13 September 2022, user @C7XWiki: added a line of text about simplification orderings. He provided an in-line citation. However, the in-line citation to Transfinite Ordinals and Their Notations: For The Uninitiated (2008, p.8) does not appear to me to be a Wikipedia:Reliable sources. JRSpriggs (talk) 20:15, 15 September 2022 (UTC)

Sorry about that, over the past few days I've been looking for a better reference, but I can't find the Dershowitz-Okada reference alluded to in Transfinite Ordinals and Their Notations. C7XWiki (talk) 10:54, 21 September 2022 (UTC)

@JRSpriggs Not about the Small Veblen ordinal, but I think I have found a reference for a similar fact, that any recursive path orderings whose function symbols are ordered in type <Γ₀ can be extended to a well-order of order type <Γ₀. Is this reference good enough justification for putting this claim on Feferman-Schutte ordinal? [1] (pp.98--99) C7XWiki (talk) 06:29, 1 October 2022 (UTC)

Go ahead. Although I did see an error, namely that it leaves out the ω in φ₀(β)=ω^β when defining the Veblen heirarchy, it is peer reviewed by the Journal of Symbolic Logic and has corrections at the end. So it passes the test for a reliable source, in my opinion. You do not need to ask my permission, in any case. JRSpriggs (talk) 18:57, 1 October 2022 (UTC)