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A countable dense homogeneous set of reals of size ℵ₁

Ilijas Farah; Michael Hrušák; Carlos Azarel Martínez Ranero — 2005

Fundamenta Mathematicae

We prove there is a countable dense homogeneous subspace of ℝ of size ℵ₁. The proof involves an absoluteness argument using an extension of the $L_{ω ₁ ω} (Q)$ logic obtained by adding predicates for Borel sets.

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