Talk:Jónsson cardinal

Wrong definition?
The definition given appears to be wrong; it is equivalent to weak compactness. Ben Standeven 21:37, 27 June 2006 (UTC)
 * I've looked it up in Kanamori, but I may be misremembering it. Ben Standeven 22:29, 16 August 2006 (UTC)
 * I do not know about the old definition, but your new one cannot be right. If the range of the function is allowed to be &kappa;, then the function can be chosen to be one-to-one and thus not homogeneous on any subset larger than cardinality 1 (certainly not &kappa;). So I will revert you. JRSpriggs 02:33, 17 August 2006 (UTC)
 * Yeah; I basically had it right, but the partition symbol he was using wasn't the standard one. Ben Standeven 22:29, 19 August 2006 (UTC)

Did you mean to say "An uncountable cardinal number κ is said to be Jónsson if for every function f: [κ] < ω → κ there is a set H of order type κ such that for each n, f restricted to n-element subsets of H omits at least one value in κ." with subsets of H? Or is H now superfluous? JRSpriggs 07:35, 20 August 2006 (UTC)
 * Oh, yeah; f omits values on H, not necessarily on kappa. I'll fix that. Ben Standeven 02:11, 24 August 2006 (UTC)

The definition given is not that in Kanamori. There, the range of f on [H] < ω omits at least one value in κ. That seems to be stronger than the definition given here, namely that the range of f on [H] n omits at least one value in κ, for each n. Perhaps they're equivalent. But I couldn't find a statement or proof of this in Kanamori or Jech. — Preceding unsigned comment added by 2001:9E8:9B33:E00:B9E2:DFCC:17B0:3193 (talk) 09:20, 11 September 2023 (UTC)