1. CMB 2013 (vol 57 pp. 119)
2. CMB 2012 (vol 57 pp. 61)
 Geschke, Stefan

2dimensional Convexity Numbers and $P_4$free Graphs
For $S\subseteq\mathbb R^n$ a set
$C\subseteq S$ is an $m$clique if the convex hull of no $m$element subset of
$C$ is contained in $S$.
We show that there is essentially just one way to construct
a closed set $S\subseteq\mathbb R^2$ without an uncountable
$3$clique that is not the union of countably many convex sets.
In particular, all such sets have the same convexity number;
that is, they
require the same number of convex subsets to cover them.
The main result follows from an analysis of the convex structure of closed
sets in $\mathbb R^2$ without uncountable 3cliques in terms of
clopen, $P_4$free graphs on Polish spaces.
Keywords:convex cover, convexity number, continuous coloring, perfect graph, cograph Categories:52A10, 03E17, 03E75 

3. CMB 2009 (vol 52 pp. 303)
 Shelah, Saharon

A Comment on ``$\mathfrak{p} < \mathfrak{t}$''
Dealing with the cardinal invariants ${\mathfrak p}$ and
${\mathfrak t}$ of the continuum, we prove that
${\mathfrak m}={\mathfrak p} = \aleph_2\ \Rightarrow\ {\mathfrak t} =\aleph_2$.
In other words, if ${\bf MA}_{\aleph_1}$ (or a weak version of
this) holds, then (of course $\aleph_2\le {\mathfrak p}\le
{\mathfrak t}$ and) ${\mathfrak p}=\aleph_2\ \Rightarrow\
{\mathfrak p}={\mathfrak t}$. The proof is based on a criterion
for ${\mathfrak p}<{\mathfrak t}$.
Categories:03E17, 03E05, 03E50 
