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An introduction to Pmax forcing Paul B. Larson

Summary: An introduction to Pmax forcing
Paul B. Larson
October 27, 2009
0.1 Pre-introduction
These notes are an account of a six-hour 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.


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University


Collections: Mathematics