http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/ Dedicated to the mathematical arts. Sat, 13 Mar 2010 15:11:00 +0000 http://wordpress.org/?v=2.7.1 hourly 1 http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/comment-page-1/#comment-54749 Walt Sat, 25 Aug 2007 17:09:13 +0000 http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/#comment-54749 Dwarf Mammoth. Dwarf Mammoth.

]]> http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/comment-page-1/#comment-54736 Ars Mathematica » Blog Archive » Suslin trees Sat, 25 Aug 2007 05:44:35 +0000 http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/#comment-54736 [...] Ars Mathematica Dedicated to the mathematical arts. « Aronszajn trees [...] [...] Ars Mathematica Dedicated to the mathematical arts. « Aronszajn trees [...]

]]> http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/comment-page-1/#comment-54732 Walt Sat, 25 Aug 2007 03:38:43 +0000 http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/#comment-54732 Kenny, that'll be today's post. Kenny, that’ll be today’s post.

]]> http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/comment-page-1/#comment-54728 Jonathan Vos Post Sat, 25 Aug 2007 01:06:53 +0000 http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/#comment-54728 Is a "relatively small large cardinal" more like a Jumbo Shrimp or a Dwarf Mammoth? Is a “relatively small large cardinal” more like a Jumbo Shrimp or a Dwarf Mammoth?

]]> http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/comment-page-1/#comment-54725 Kenny Easwaran Fri, 24 Aug 2007 18:48:45 +0000 http://www.arsmathematica.net/archives/2007/08/23/aronszajn-trees/#comment-54725 Yeah, Aronszajn trees really ought not to exist, but you can get used to them. The really weird ones are Suslin (or Souslin) trees. Not only is each level countable, but so is each anti-chain. I know that it's consistent that Suslin trees don't exist - but I think it's also consistent that they do (at least, assuming the consistency of some relatively small large cardinal). Yeah, Aronszajn trees really ought not to exist, but you can get used to them. The really weird ones are Suslin (or Souslin) trees. Not only is each level countable, but so is each anti-chain. I know that it’s consistent that Suslin trees don’t exist - but I think it’s also consistent that they do (at least, assuming the consistency of some relatively small large cardinal).

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