Applications of omega_1-approximation systems
by
David Milovich
University of Wisconsin---Madison

Under some mild assumptions, a transfinite sequence of countable elementary substructures of the universe can be uniformly expressed as a finite union of (possibly uncountable) elementary substructures of the universe. One version of this representation was used by Jackson and Mauldin to prove there is a subset of R^2 that meets every isometric copy of Z^2 at exactly one point. I have used the representation to prove order-theoretic results about subsets of free boolean algebras and families of subsets of dyadic compacta. These results also generalize from omega_1 to arbitrary uncountable regular cardinals.

Date received: March 10, 2008