A countable dense homogeneous set of reals of size $\aleph_1$
Volume 186 / 2005
Fundamenta Mathematicae 186 (2005), 71-77
MSC: 54E52, 54H05, 03E15.
DOI: 10.4064/fm186-1-5
Abstract
We prove there is a countable dense homogeneous subspace of $\Bbb R$ of size~$\aleph_1$. The proof involves an absoluteness argument using an extension of the $L_{\omega_1\omega}(Q)$ logic obtained by adding predicates for Borel sets.
