Περίληψη:
We prove a density version of the Halpern-Läuchli Theorem. This settles in the affirmative a conjecture of R. Laver.Specifically, let us say that a tree T is homogeneous if T has a unique root and there exists an integer b ≥ 2 such that every t ∈ T has exactly b immediate successors. We show that for every d ≥ 1 and every tuple (T1., T d) of homogeneous trees, if D is a subset of the level product of (T1., T d) satisfying lim supn→∞|D∩(T1(n)×⋯×Td(n))||T1(n)×⋯×Td(n)|>0 then there exist strong subtrees (S1., S d) of (T1., T d) having a common level set such that the level product of (S1., S d) is a subset of D. © 2013 The Authors.
Συγγραφείς:
Dodos, P.
Kanellopoulos, V.
Karagiannis, N.
