Set theoretic topology is the area of mathematics where the techniques of logic and combinatorics are utilized to investigate the topological structure of spaces. The methods of logic are necessary because many fundamental questions of point set topology cannot be answered within the usual axioms of set theory. In other words, certain statements are neither provable nor refutable without appealing to extra axioms. Fleissner intends to use methods of set theory, especially forcing, large cardinals, and the structure of Godel's constructible universe, to prove theorems and create counterexamples in the theory of topology, and related areas of combinatorics and Boolean algebras.
