Proximity to lp and c0 in Banach spaces

We construct a class of minimal trees and use these trees to establish a number of coloring theorems on general trees. Among the applications of these trees and coloring theorems are quantification of the Bourgain l(p) and c(0) indices, dualization of the Bourgain c(0) index, establishing sharp positive and negative results for constant reduction, and estimating the Bourgain l(p) index of an arbitrary Banach space X in terms of a subspace Y and the quotient X/Y. (C) 2015 Elsevier Inc. All rights reserved.