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In mathematical set theory, an Aronszajn line is a linear ordering of cardinality ℵ 1 {\displaystyle \aleph _{1}} which contains no subset order-isomorphic to
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.
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