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]

References

Шаблон:Settheory-stub