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Aronszajn tree
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(Definition)
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A $\kappa$ tree $T$ for which $|T_\alpha|<\kappa$ for all $\alpha<\kappa$ and which has no cofinal branches is called a $\kappa$ Aronszajn tree. If $\kappa=\omega_1$ then it is referred to simply as an Aronszajn tree.
If there are no $\kappa$ Aronszajn trees for some $\kappa$ then we say $\kappa$ has the tree property. $\omega$ has the tree property, but no singular cardinal has the tree property.
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"Aronszajn tree" is owned by Henry.
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Cross-references: singular cardinal, cofinal branches
There are 4 references to this entry.
This is version 7 of Aronszajn tree, born on 2002-07-27, modified 2006-06-24.
Object id is 3217, canonical name is Aronszajn.
Accessed 7460 times total.
Classification:
| AMS MSC: | 05C05 (Combinatorics :: Graph theory :: Trees) | | | 03E05 (Mathematical logic and foundations :: Set theory :: Other combinatorial set theory) |
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Pending Errata and Addenda
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