Set theory is a branch of mathematical logic .
At one time, set theory was regarded as an encapturing universal theory behind mathematics, whose role was to axiomatize the way we think in mathematics. Although we have known for many years that a perfection in this direction is provably impossible, the fundamental results obtained in this search have opened many new branches in set-theory, like independence results and fine structure theory.
Having concluded that there is no perfect axiom scheme, it is still true that most of classical mathematics takes place within a particular system known as ZFC. So, much of set theory is devoted to the study of this scheme, using both methods for proving ZFC theorems, like infinite combinatorics and pcf theory, and the ones to show that no ZFC result is possible, that is the independence proofs. Many questions which can be formulated in simple combinatorial terms, like if cardinal arithmetic is trivial, need so called large cardinals to become interesting. That is why modern set theory is deeply hinged on the study of large cardinals, in addition to the study of ZFC. Additional important areas of set theory are determinacy axioms, inner model theory and descriptive set theory, to mention but a few.
By its nature, set theory is deeply connected with other branches of mathematics. Discovering new set-theoretic properties has often been inspired by a question from another field of mathematics, and vice versa, a new theory inside of set theory has often been tested by finding applications of that theory to questions from the outside. Some fields in which set theory has been applied more recently are set-theoretic topology, Boolean algebras, measure theory and Abelian group theory. Within mathematical logic, there is a strong link between set theory and model theory.
Research activity in set theory at UEA includes proper forcing, pcf, set-theoretic topology and measure theory, set-theoretic model theory, infinite combinatorics and large cardinals forcing. To get more information about set theory, you can consult: