Partition ideals below $\aleph _{\omega} $

Volume 217 / 2012

P. Dodos, J. Lopez-Abad, S. Todorcevic Fundamenta Mathematicae 217 (2012), 21-34 MSC: Primary 03E35; Secondary 03E02, 03E55. DOI: 10.4064/fm217-1-3

Abstract

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.

Authors

  • P. DodosDepartment of Mathematics
    University of Athens
    Panepistimiopolis 157 84, Athens, Greece
    e-mail
  • J. Lopez-AbadInstituto de Ciencias Matemáticas
    CSIC-UAM-UC3M-UCM
    C/ Nicolás Cabrera, n$^{\circ }$ 13-15
    Campus Cantoblanco UAM
    28049 Madrid, Spain
    e-mail
  • S. TodorcevicInstitut 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
    e-mail

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