Summary: ITERATED FORCING AND THE CONTINUUM HYPOTHESIS
Appalachian Set Theory Workshop, May 2930, 2009
Lectures by Todd Eisworth and Justin Tatch Moore
Notes taken by David Milovich
Remark. The notes which follow reflect the content of a two day tutorial which took
place at the Fields Institute on 5/29 and 5/30 in 2009. Most of the content has
existed in the literature for some time (primarily in the original edition of ) but
has proved difficult to read and digest for various reasons. The only new material
contained in these lectures concerns the notion of a fusion scheme presented in
Sections 6 and 7 and even this has more to do with style than with mathematics.
Our presentation of the iteration theorems follows . The k-iterability condition is
a natural extrapolation of what appears in  and , where the iteration theorem
for the 0-iterability condition is presented (with a weakening of < 1-properness).
The formulation of complete properness is taken from . We stress, however, these
definitions and theorems are really technical and/or pedagogical modifications of
the theorems and definitions of Shelah presented in . Those interested in further
reading on the topic of the workshop should consult: , , , , , and
. We would like to thank the anonymous referee for their careful reading and
suggesting a number of improvements.