Working with Nonstandard Models
Most of the research in foundations of mathematics that I do in some way or another involves the use of nonstandard models. I will give a few examples, and indicate what is involved.
Compact covering mappings between borel sets and the size of constructible reals
We prove that the topological statement: Any compact covering mapping between two Borel sets is inductively perfect is equivalent to the set-theoretical statement: ∀α E ω ω , N L(α) 1 < N 1 .
Countable-compact-covering maps and compact-covering maps
Abstract We show that every countable-compact-covering map with compact fibers from a separable metric space X onto a first-countable, regular space Y is compact-covering. We also show that the assumption that ƒ is countable-compact-covering cannot be replaced by a weaker condition.