Countable dense homogeneous spaces under Martin’s axiom
- Cite this article as:
- Baldwin, S. & Beaudoin, R.E. Israel J. Math. (1989) 65: 153. doi:10.1007/BF02764858
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.