A Result in Dual Ramsey Theory

We present a result which is obtained by combining a result of Carlson with the Finitary Dual Ramsey Theorem of Graham-Rothschild. We start by introducing some notation. We conform to the usual practice of identifying the least infinite ordinal with the set of non-negative integers. Given , , a partition of into blocks is an onto function X : such that min X-1 ({n}) < min X-1 ({m}) whenever n < m < . Thus, the blocks of X are ordered as their leaders (i.e., their least elements). The leader function : ()

• Type: Journal
• Year: 2002
• Where: JCT
• Authors: Lorenz Halbeisen, Pierre Matet
• Keywords: Dual Ramsey Theorem, Finitary Dual Ramsey, JCT 2002, Min X-1