Geodesic
Partition ideals below $\aleph _{\omega} $
P. Dodos1 ; J. Lopez-Abad2 ; S. Todorcevic3
1 Department of Mathematics University of Athens Panepistimiopolis 157 84, Athens, Greece
2 Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM C/ Nicolás Cabrera, n$^{\circ }$ 13-15 Campus Cantoblanco UAM 28049 Madrid, Spain
3 Institut de Mathématiques de Jussieu CNRS-UMR 7586 2 place Jussieu – Case 7012 72521 Paris Cedex 05, France and Department of Mathematics University of Toronto Toronto, Canada, M5S 2E4
Fundamenta Mathematicae, Tome 217 (2012) no. 1, pp. 21-34 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Motivated by an application to the unconditional basic sequence problem appearing in our previous paper, we introduce analogues of the Laver ideal on $\aleph _2$ living on index sets of the form $[\aleph _k]^\omega $ and use this to refine the well-known high-dimensional polarized partition relation for $\aleph _\omega $ of Shelah.
DOI : 10.4064/fm217-1-3
Keywords: motivated application unconditional basic sequence problem appearing previous paper introduce analogues laver ideal aleph living index sets form aleph omega refine well known high dimensional polarized partition relation aleph omega shelah

P. Dodos 1 ; J. Lopez-Abad 2 ; S. Todorcevic 3

1 Department of Mathematics University of Athens Panepistimiopolis 157 84, Athens, Greece
2 Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM C/ Nicolás Cabrera, n$^{\circ }$ 13-15 Campus Cantoblanco UAM 28049 Madrid, Spain
3 Institut de Mathématiques de Jussieu CNRS-UMR 7586 2 place Jussieu – Case 7012 72521 Paris Cedex 05, France and Department of Mathematics University of Toronto Toronto, Canada, M5S 2E4 
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P. Dodos; J. Lopez-Abad; S. Todorcevic. Partition ideals below $\aleph _{\omega} $. Fundamenta Mathematicae, Tome 217 (2012) no. 1, pp. 21-34. doi: 10.4064/fm217-1-3

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