 
Summary: An introduction to Pmax forcing
Paul B. Larson
October 27, 2009
0.1 Preintroduction
These notes are an account of a sixhour lecture series I presented at Carnegie
Mellon University on September 9, 2006, at the inaugural meeting of the Ap
palachian Set Theory series. My remarks (occasionally improvised) were faith
fully transcribed by Peter LeFanu Lumsdaine and Yimu Yin, who then presented
me with a rough draft of this article. Their account aimed to capture the feel
of the discussions (including some direct quotations), and I've tried to preserve
that as much as possible.
1 Introduction
The forcing construction Pmax was invented by W. Hugh Woodin in the early
1990's in the wake of his result that the saturation of the nonstationary ideal
on 1 (NS1
) plus the existence of a measurable cardinal implies that there
is a definable counterexample to the Continuum Hypothesis (in particular, it
implies that 1
2 = 2, which implies ¬CH). These notes outline a proof of the
2 maximality of the Pmax extension, which we can state as follows.
