Aronszajn line

In mathematical set theory, an Aronszajn line (named after Nachman Aronszajn) 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]

References

  1. Funk, Will; Lutzer, David J. (2005). "Lexicographically ordered trees". Topology and Its Applications. 152 (3): 275–300. doi:10.1016/j.topol.2004.10.011. Zbl 1071.03032.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.