Abstract
Abstract
The Halpern–Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial essence of this proof, we isolate various partition principles about products of perfect Polish spaces. These principles yield straightforward proofs of the Halpern–Läuchli theorem, and the same forcing from Harrington’s proof can force their consistency. We also show that these principles are not ZFC theorems by showing that they put lower bounds on the size of the continuum.
Publisher
Cambridge University Press (CUP)
Reference24 articles.
1. [1] Bannister, N. , Bergfalk, J. , Moore, J. T. , and Todorcevic, S. , A descriptive approach to higher derived limits, preprint, 2022. arXiv:2203.00165.
2. Simultaneously vanishing higher derived limits without large cardinals
3. A partition theorem for a large dense linear order
4. Monochromatic sumset without large cardinals
5. [6] Dobrinen, N. and Hathaway, D. , The Halpern–Läuchli theorem at a measurable cardinal, this Journal, vol. 82 (2017), no. 4, pp. 1560–15752017. MR 3743623