A new proof of the 2-dimensional Halpern–Läuchli Theorem
نویسنده
چکیده
We provide an ultrafilter proof of the 2-dimensional Halpern–Läuchli Theorem in the following sense. If T0 and T1 are trees and T0 ⊗ T1 denotes their level product, we exhibit an ultrafilter U ∈ β(T0 ⊗ T1) so that every A ∈ U contains a subset of the form S0 ⊗ S1 for suitable strong subtrees of T0 and T1. We then discuss obstacles to extending our method of proof to higher dimensions.
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