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- Title
THE HALPERN–LÄUCHLI THEOREM AT A MEASURABLE CARDINAL.
- Authors
DOBRINEN, NATASHA; HATHAWAY, DAN
- Abstract
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.
- Subjects
CARDINALS (Clergy); DISCRIMINANT analysis; NONCLASSICAL mathematical logic; APPLIED mathematics; ALGEBRAIC logic
- Publication
Journal of Symbolic Logic, 2017, Vol 82, Issue 4, p1560
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2017.31