Countable dense homogeneous spaces under Martin's axiom
A separable space \(X\) is said to be CDH if for any two countable dense subsets \(A\) and \(B\) of \(X\) there is an autohomeomorphism \(f\) of \(X\) such that \(f(A)=B\). The authors discuss CDH subspaces of the reals under various versions of Martin's axiom. For example, it is shown that Martin's axiom for countable partial orders implies the existence of a Bernstein set which is CDH.
scientific article; zbMATH DE number 4103941