My question is about terminology:

Do you know why stationary sets were named such?

Going over the following MO question about the intuition behind stationary sets, the only compelling argument I can think of is Fodor's lemma.

Is this the reason?

  • 5
    $\begingroup$ Ioannis, this was addressed in MSE. They were also referred early on as Mahlo sets. $\endgroup$ Commented Jul 26, 2013 at 0:16
  • $\begingroup$ @Andres: Thank you for the link. It indeed answers the question. I never seem to look MSE for some reason. $\endgroup$ Commented Jul 26, 2013 at 13:39

1 Answer 1


In Infinite Combinatorics, in: Handbook of the History of Logic, 6. Sets and Extensions in the Twentieth Century, p 226, footnote 214, Jean Larson states that the term was first used in G. Bloch: Sur les ensembles stationnaires de nombres ordinaux et les suites distinguees de fonctions regressives, Comptes Rendus Acad. Sci Paris, 236(1953), 265-268. The reason for the name was probably Neumer's theorem, a weaker and earlier form of Fodor's theorem.

  • $\begingroup$ Indeed. Neumer's theorem states that if $S$ is a stationary subset of a cardinal $\rho$ of uncountable cofinality, and $f:S\to\rho$ is regressive, then $f$ is bounded on a cofinal set, that is, there is an $\alpha<\rho$, and a $D\subset S$, $D$ cofinal, such that $f(\beta)<\alpha$ for all $\beta\in D$. The reference is W. Neumer. Verallgemeinerung eines Satzes von Alexandroff und Urysohn, Math. Z., 54, (1951), 254—261. MR0043860 (13,331a). $\endgroup$ Commented Jul 26, 2013 at 6:36
  • $\begingroup$ Actually, Bloch's precise statement is a bit more cumbersome than I mentioned. He uses a notion similar to club, that he calls a band: Instead of requiring that $C\subset\rho$ is cofinal, he requires that it has order type $\rho$. Such $C$ he calls full parts, and bands are sets that are closed full parts. The theorem mentioned in the title of Neumer's paper is a particular case of a result of Dushnik from the early 1930s. (The version I stated above is a modern reformulation. Juhász proved in the 70s that it is essentially a topological result.) $\endgroup$ Commented Jul 26, 2013 at 6:40
  • $\begingroup$ Hmm... Bloch closes his note mentioning Neumer's paper, but what it says is: "Cet article ne m'était pas connu quand j'ai rédigé la présente Note." Other than this, Bloch's article includes no references. $\endgroup$ Commented Jul 26, 2013 at 7:04
  • 4
    $\begingroup$ @Andres: So these bands, do they play in any clubs? Or do they move from town to town too fast for such gigs? (i.e. are they non-stationary?) :-) $\endgroup$
    – Asaf Karagila
    Commented Jul 26, 2013 at 9:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.