Talk:Mahlo cardinal
Latest comment: 12 years ago by JRSpriggs in topic Correct pronunciation
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So what does stationary set mean here? edit
In this article, the term stationary set set is used in the definition of Mahlo cardinal. It's linked, which is good, but the linked article offers three distinct notions of stationary. Which one is the one to use? YohanN7 (talk) 18:47, 11 May 2011 (UTC)
- We are talking about the classical notion, as is almost always the case. This is the simplest notion. Whenever one is talking about subsets of ordinals (rather than, say, subsets of the power set of an ordinal), then the classical notion is being used.
- So for our purposes, a stationary set is a set which always has a nonempty intersection with any closed unbounded set. Where "set" here means a subset of a fixed ordinal, κ, which has uncountable cofinality. JRSpriggs (talk) 01:10, 12 May 2011 (UTC)
- Ok, thanks. I think it would be nice to somehow get this into the article. I'm probably not the only one the will wonder. Simplest and ugliest would be to add a parenthetical remark:
- A cardinal number κ is called Mahlo if κ is inaccessible and the set U = {λ < κ: λ is inaccessible} is stationary (in the classical sense) in κ.
- Better in my opinion would be to include (parts of) the explanation you gave above:
- A stationary set is a set which always has a nonempty intersection with any closed unbounded set.
- A cardinal number κ is called Mahlo if κ is inaccessible and the set U = {λ < κ: λ is inaccessible} is stationary in κ.
Correct pronunciation edit
Can anybody please give the correct pronunciation of Mahlo in IPA? VladimirReshetnikov (talk) 21:43, 10 February 2012 (UTC)
- The pronunciation may vary some depending on how the vowels are pronoucned; the first vowel in particular has a lot of realizations in the US. But I would pronounce the name as /mɑloʊ/, I believe. — Carl (CBM · talk) 00:55, 11 February 2012 (UTC)
- Notice that Paul Mahlo was German, if that affects the pronunciation. JRSpriggs (talk) 09:11, 11 February 2012 (UTC)