Leocat
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grammar edit
Regarding this edit[1], hahahahhaha, that is classic. Thanks. HighInBC 01:04, 18 October 2006 (UTC)
Continuum hypothesis edit
Hi Leocat,
so what you wrote at continuum hypothesis is kind of a natural mistake, but still wrong. I'm guessing you're thinking of CH as saying "there is no set of reals of cardinality strictly between that of the naturals and that of the reals", and so you'd think if you have more sets of reals, then you have more chance to find such a set.
What you're missing is that the smaller model and the larger one may not agree on whether a given set of reals has the same cardinality as R. Given a fixed set of reals X that's in both models, it's the larger model that might have a bijection between X and R, when the smaller one doesn't.
It actually works in exactly the opposite direction from what you might have thought. If N and M are two transitive models of ZFC both containing all the reals, with N contained in M, then if N satisfies CH, then M must also satisfy CH. But the reverse is not true. --Trovatore 06:48, 20 October 2006 (UTC)
Responded to your latest remarks on my talk page. --Trovatore 19:03, 21 October 2006 (UTC)