1. CMB 2013 (vol 57 pp. 119)
2. CMB 2011 (vol 56 pp. 317)
 Dorais, François G.

A Note on Conjectures of F. Galvin and R. Rado
In 1968, Galvin conjectured that an uncountable poset $P$ is the
union of countably many chains if and only if this is true for every
subposet $Q \subseteq P$ with size $\aleph_1$. In 1981, Rado
formulated a similar conjecture that an uncountable interval graph $G$ is countably
chromatic if and only if this is true for every induced subgraph $H
\subseteq G$ with size $\aleph_1$. TodorÄeviÄ has shown
that Rado's Conjecture is consistent relative to the existence of a
supercompact cardinal, while the consistency of Galvin's Conjecture
remains open. In this paper, we survey and collect a variety of
results related to these two conjectures. We also show that the
extension of Rado's conjecture to the class of all chordal graphs is
relatively consistent with the existence of a supercompact cardinal.
Keywords:Galvin conjecture, Rado conjecture, perfect graph, comparability graph, chordal graph, cliquecover number, chromatic number Categories:03E05, 03E35, 03E55 

3. CMB 2010 (vol 54 pp. 270)
 Dow, Alan

Sequential Order Under PFA
It is shown that it follows from PFA
that there is no
compact scattered space of height greater than $\omega$
in which the sequential order and the scattering heights coincide.
Keywords:sequential order, scattered spaces, PFA Categories:54D55, 03E05, 03E35, 54A20 

4. 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 

5. CMB 2008 (vol 51 pp. 579)
 Matet, Pierre

Guessing with Mutually Stationary Sets
We use the mutually stationary sets of Foreman and Magidor
as a tool to establish the validity of the twocardinal version
of the diamond principle in some special cases.
Keywords:$P_\kappa(\lambda)$, diamond principle Category:03E05 

6. CMB 1999 (vol 42 pp. 13)
 Brendle, Jörg

Dow's Principle and $Q$Sets
A $Q$set is a set of reals every subset of which is a relative
$G_\delta$. We investigate the combinatorics of $Q$sets and
discuss a question of Miller and Zhou on the size $\qq$ of the smallest
set of reals which is not a $Q$set. We show in particular that various
natural lower bounds for $\qq$ are consistently strictly smaller than
$\qq$.
Keywords:$Q$set, cardinal invariants of the continuum, pseudointersection number, $\MA$($\sigma$centered), Dow's principle, almost disjoint family, almost disjointness principle, iterated forcing Categories:03E05, 03E35, 54A35 
