Konstantinos Tyros

A density version of the Carlson–Simpson theorem

We prove a density version of the Carlson--Simpson Theorem. Specifically we show the following. For every integer

Dense Subsets of Products of Finite Trees

k\geq 2

Measurable events indexed by products of trees

and every set

Oscillation stability for continuous monotone surjections

A

On colorings of variable words

of words over

Combinatorial Structures on van der Waerden sets

k

MEASURABLE EVENTS INDEXED BY WORDS

satisfying \[\limsup_{n\to\infty} \frac{|A\cap [k]^n|}{k^n}>0\] there exist a word

A Simple Proof of the Density Hales–Jewett Theorem

c

Finite order spreading models

over

Higher order spreading models

k