A countable dense homogeneous set of reals of size ℵ₁
Ilijas Farah ; Michael Hrušák ; Carlos Azarel Martínez Ranero
Fundamenta Mathematicae, Tome 185 (2005), p. 71-77 / Harvested from The Polish Digital Mathematics Library
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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 Lω₁ω(Q) logic obtained by adding predicates for Borel sets.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:282770 
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     title = {A countable dense homogeneous set of reals of size 1},
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Ilijas Farah; Michael Hrušák; Carlos Azarel Martínez Ranero. A countable dense homogeneous set of reals of size ℵ₁. Fundamenta Mathematicae, Tome 185 (2005) pp. 71-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-1-5/