Geodesic
A countable dense homogeneous set of reals of size $\aleph_1$
Ilijas Farah1 ; Michael Hrušák2 ; Carlos Azarel Martínez Ranero2
1 Department of Mathematics and Statistics York University 4700 Keele Street Toronto, Canada M3J 1P3 and Matematicki Institut Kneza Mihaila 35 11000 Beograd Serbia and Montenegro
2 Instituto de Matemáticas UNAM Unidad Morelia, A.P. 61-3 Xangari, C.P. 58089 Morelia, Mich., México
Fundamenta Mathematicae, Tome 186 (2005) no. 1, pp. 71-77.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm186-1-5
Keywords: prove there countable dense homogeneous subspace bbb size aleph proof involves absoluteness argument using extension omega omega logic obtained adding predicates borel sets

Ilijas Farah 1 ; Michael Hrušák 2 ; Carlos Azarel Martínez Ranero 2

1 Department of Mathematics and Statistics York University 4700 Keele Street Toronto, Canada M3J 1P3 and Matematicki Institut Kneza Mihaila 35 11000 Beograd Serbia and Montenegro
2 Instituto de Matemáticas UNAM Unidad Morelia, A.P. 61-3 Xangari, C.P. 58089 Morelia, Mich., México 
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Ilijas Farah; Michael Hrušák; Carlos Azarel Martínez Ranero. A countable dense homogeneous set of reals of size $\aleph_1$. Fundamenta Mathematicae, Tome 186 (2005) no. 1, pp. 71-77. doi : 10.4064/fm186-1-5. http://geodesic.mathdoc.fr/articles/10.4064/fm186-1-5/

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