Possible Topics for Math 597D Computability 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 theory 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