From $\aleph_2$ to infinity
May 15 to May 19, 2023
at the
American Institute of Mathematics,
San Jose, California
organized by
James Cummings,
Itay Neeman,
and Dima Sinapova
Original Announcement
This workshop is devoted to combinatorial problems about infinite cardinals. There are two types of infinite cardinals to investigate: successors of regular cardinals, most notably $\aleph_2$, and successors of singular cardinals, for example ${\aleph_{\omega+1}}_{\omega+1}$. The workshop will focus on combinatorial principles such as the tree property, stationary reflection and the effect of consequences on forcing axioms on cardinal arithmetic, in particular what implications they have on the continuum, and the singular cardinal hypothesis (SCH).
The main topics of the workshop are

The tree property, its strengthening ITP, stationary reflection how these combinatorial principles interact with SCH;

Which consequences of PFA and MM require the continuum to be $\aleph_2$, and more generally, their effect on cardinal arithmetic;

Forcing techniques such as proper iterated forcing and Prikry type forcing.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.