22 research outputs found
A partially non-proper ordinal beyond L(V \u3bb+1)
In his recent work, Woodin has defined new axioms stronger than I0 (the existence of an elementary embedding from to itself), that involve elementary embeddings between slightly larger models. There is a natural correspondence between I0 and Determinacy, but to extend this correspondence in the new framework we must insist that these elementary embeddings are proper. Previous results validated the definition, showing that there exist elementary embeddings that are not proper, but it was still open whether properness was determined by the structure of the underlying model or not. This paper proves that this is not the case, defining a model that generates both proper and non-proper elementary embeddings, and compare this new model to the older ones
Set Theory
This workshop included selected talks on pure set theory and its applications, simultaneously showing diversity and coherence of the subject
In Search of Ultimate-L the 19th Midrasha Mathematicae Lectures
We give a fairly complete account which first shows that the solution to the inner model problem for one supercompact cardinal will yield an ultimate version of L and then shows that the various current approaches to inner model theory must be fundamentally altered to provide that solution.Mathematic
Full normalization for mouse pairs
We develop the theory of meta-iteration trees, that is, iteration trees whose
base "model" is itself an ordinary iteration tree. We prove a comparison
theorem for meta-iteration strategies parallel to the one for ordinary
iteration strategies, and use it to show that the iteration strategy component
of a mouse pair condenses to itself under weak tree embeddings. These
constitute a class of embeddings between iteration trees that is significantly
larger than the class of embeddings mentioned in the definition of mouse pair.
We then use this very strong hull condensation property of mouse pairs to show
that every iterate of a mouse pair is an iterate via a single -tight,
normal iteration tree, and that the associated tail strategies are independent
of how the iterate was reached.Comment: 105 page