Subsets of cardinals in a well-ordering
- From: Justin Palumbo <justinpa84@xxxxxxxxx>
- Date: 23 May 2007 11:32:33 -0700
(from Kunen - exercise 19) Let kappa be an infinite cardinal, let W
well-order kappa. Prove there's a subset X of kappa with cardinality
kappa on which W agrees with the usual ordering of ordinals.
One way to rephrase this is that any kappa length sequence of distinct
ordinals less than kappa has an increasing subsequence of length
kappa.
I can prove it for regular cardinals easily enough, but I'm pretty
much stumped on proving it for the more general case (although I've
reduced it to several statements trying some other strategies, but I
think these are deadends).
.
- Follow-Ups:
- Re: Subsets of cardinals in a well-ordering
- From: Robert Sheskey
- Re: Subsets of cardinals in a well-ordering
- Prev by Date: Re: Can We Quantify over Everything?
- Next by Date: Re: implications of false axioms
- Previous by thread: Call For Participation: WORLDCOMP'07: joint conferences in CS, CE, and applied computing, June 25-28, 2007, Las Vegas
- Next by thread: Re: Subsets of cardinals in a well-ordering
- Index(es):
Relevant Pages
|
