A density version of the Carlson-Simpson theorem

作者：Dodos Pandelis^*; Kanellopoulos Vassilis; Tyros Konstantinos

来源：Journal of the European Mathematical Society, 2014, 16(10): 2097-2164.

DOI：10.4171/JEMS/484

• Words
• left variable words
• density

We prove a density version of the Carlson Simpson Theorem. Specifically we show the following.
For every integer k >= 2 and every set A of words over k satisfying
n ->infinity Jim sup vertical bar A boolean AND [k](n)vertical bar/k(n) > 0
there exist a word c over k and a sequence (w(n)) of left variable words over k such that the set
{c} boolean OR {c(boolean AND) w(0)(a(0))(boolean AND) ... (boolean AND) w(n)(a(n)) : n is an element of N and a(0), ..., a(n) is an element of [k]}
is contained in A.
While the result is infinite-dimensional, its proof is based on an appropriate finite and quantitative version, also obtained in the paper.

• 出版日期2014