Talk:Aronszajn line

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Mathematics rating:	Stub Class	Low Priority	Field: Foundations, logic, and set theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 21:12, 21 May 2007 (UTC)

As much as I know this is called a Specker type. Kope 13:27, 13 May 2007 (UTC)

Specker rediscovered this notion; Aronszajn and Kurepa were the first to construct such a linear order. See Kurepa's work in the 1930's. For some reason the Aronszajn tree was remembered as a violation of Konig's lemma at the level of $\omega$/$\omega_1$ but its relationship to linear orders was forgotten. This is strange since the pioneering work on set-theoretic trees (again mostly due to Kurepa in the 30s-50s) was clearly motivated by the study of linear orders (and Souslin's problem in particular). All of this history is carefully spelled out in Todorcevic's article on trees and linear orders in the "Handbook of Set-Theoretic Topology". 70.16.59.28 01:43, 25 October 2007 (UTC)justin

Is it part of Wikipedia's policy to rename misnamed notions? Kope 04:32, 25 October 2007 (UTC)

I don't know Wikipedia's policy on the matter. In Todorcevic's article, he reclaims the use of "Aronszajn line" to reflect historical accuracy. That was roughly 25 years ago. "Aronszajn line" is now common usage. I don't see mention of "Specker type" as defensable except as a historical footnote. 71.123.20.2 (talk) 16:51, 23 December 2007 (UTC)justin