All Questions

A classic result of Sierpiński shows that $2^{\aleph_0}\nrightarrow [\aleph_1]^2_2$, that is, there is a coloring of pairs of real numbers using two colors such that both colors appear on any ...

Problem 1. Is it true that each uncountable group $G$ contains two subsets $A,B\subset G$ such that 1) for any $x,y\in G$ the intersection $xA\cap yB$ is finite and 2) for any function $\...

For $m,n,k < \omega$, consider the equation $X \to (\omega \times k)^{m}_{n}$ What is the smallest $X$ known to satisfy it? Baumgartner-Hajnal theorem gives a satisfactory answer for $m=2$, but ...

Question: Find/compute relations between the classical Ramsey numbers and their variations (described below) -- exact or asymptotic. A graph is a set $\ X\ $ together with a (coloring) function $\ c:\...