Английская Википедия:Aronszajn line
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In mathematical set theory, an Aronszajn line (named after Nachman Aronszajn) is a linear ordering of cardinality <math>\aleph_1</math> which contains no subset order-isomorphic to
- <math>\omega_1</math> with the usual ordering
- the reverse of <math>\omega_1</math>
- 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]
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