Aronszajn line
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An Aronszajn line is a linear ordering of cardinality 
which contains no subset order-isomorphic to
with the usual ordering- the reverse of
- an uncountable subset of the Real numbers with the usual ordering
Unlike Suslin lines, the existence of Aronszajn lines is provable using the standard axioms of set theory. A linear ordering is an Aronszajn line if and only if it is the lexicographical ordering of some Aronszajn tree.[1]
[edit] References
- ^ Funk, W.; Lutzer, D. (2005). "Lexicographically ordered trees". Topology and it Applications 152: 275–300. doi:.
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