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1 results

  • THE HALPERN–LÄUCHLI THEOREM AT A MEASURABLE CARDINAL

  • NATASHA DOBRINEN, DAN HATHAWAY
  • Journal:
    The Journal of Symbolic Logic / Volume 82 / Issue 4 / December 2017
    Published online by Cambridge University Press:
    09 January 2018, pp. 1560-1575
    Print publication:
    December 2017

  • Several variants of the Halpern–Läuchli Theorem for trees of uncountable height are investigated. For κ weakly compact, we prove that the various statements are all equivalent, and hence, the strong tree version holds for one tree on any weakly compact cardinal. For any finite d ≥ 2, we prove the consistency of the Halpern–Läuchli Theorem on d many normal κ-trees at a measurable cardinal κ, given the consistency of a κ + d-strong cardinal. This follows from a more general consistency result at measurable κ, which includes the possibility of infinitely many trees, assuming partition relations which hold in models of AD.