Israel Journal of Mathematics

, Volume 65, Issue 2, pp 153–164

Countable dense homogeneous spaces under Martin’s axiom

  • Stewart Baldwin
  • Robert E. Beaudoin
Article

Abstract

We show that Martin’s axiom for countable partial orders implies the existence of a countable dense homogeneous Bernstein subset of the reals. Using Martin’s axiom we derive a characterization of the countable dense homogeneous spaces among the separable metric spaces of cardinality less thanc. Also, we show that Martin’s axiom implies the existence of a subset of the Cantor set which isλ-dense homogeneous for everyλ <c.

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Copyright information

© The Weizmann Science Press of Israel 1989

Authors and Affiliations

  • Stewart Baldwin
    • 1
  • Robert E. Beaudoin
    • 1
  1. 1.Department of MathematicsAuburn UniversityAuburnUSA

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