Possible Topics for Math 597D


   register machines, computability, the Halting Problem, unsolvable
   problems in algebra, unsolvable problems in number theory, the
   Fixed Point Theorem, recursively enumerable sets, oracle
   computations, Turing reducibility, degrees of unsolvability, cones
   of Turing degrees, Pi^0_1 classes, basis theorems

 Model Theory

   the Compactness Theorem, element types, saturated models, prime
   models, stability, categoricity in power, o-minimality, finite model

 Descriptive Set Theory

   hierarchies of sets and predicates (arithmetical, hyperarithmetical,
   projective), basis theorems, Borel sets, Gandy forcing, Silver's
   Theorem on Borel equivalence relations, singular spaces, infinite
   games, Borel determinacy

 Axiomatic Set Theory

   constructibility, forcing, the Continuum Hypothesis, the Axiom of
   Choice, iterated forcing, Martin's Axiom, Ramsey's Theorem, large
   cardinals, ultrafilters and ultrapowers, measurable cardinals,
   Ramsey cardinals, supercompact cardinals, projective determinacy,
   Solovay's model

 Modal Logic

   the logic of necessity, the systems S4 and S5, the system G, Kripke
   semantics, derivability conditions, Go"del's Theorem on
   unprovability of consistency, Solovay's Completeness Theorem for G