Grant Reaber
Graduate Student
Department of Mathematical Sciences
Carnegie Mellon University

Title:

Iteration trees I

Abstract:

Iteration trees, introduced by Steel, are a generalization of linear
iterations such as the one used by Kunen in his analysis of L[U]. They
are important in inner model theory and are also used in the proof by
Martin and Steel that if there are infinitely many Woodin cardinals then
projective determinacy is true. I will develop some of the theory of
iteration trees from scratch and show how to use a Woodin cardinal to
construct a special kind of iteration tree, called an alternating chain,
that is related to the proof of projective determinacy.