MATH 557. Mathematical Logic (3) The predicate calculus. Completeness and compactness. Gödel's first and second incompleteness theorems. Introduction to model theory. Introduction to proof theory. Prerequisite: MATH 435 or 457 or equivalent.

MATH 558. Foundations of Mathematics I (3) Decidability of the real numbers. Computability. Undecidability of the natural numbers. Models of set theory. Axiom of choice. Continuum hypothesis. Prerequisite: any 400-level MATH course or equivalent.

MATH 559-560. Recursion Theory I, II (3 each) Recursive functions; degrees of unsolvability. Hyperarithmetic theory; applications to Borel combinatorics. Computational complexity. Combinatory logic and the lambda calculus. Prerequisite: MATH 459 or 557 or 558.

MATH 561-562. Set Theory I, II (3 each) Models of set theory. Inner models, forcing, large cardinals, determinacy. Descriptive set theory. Applications to analysis. Prerequisite: MATH 557 or 558.

MATH 563-564. Model Theory I, II (3 each) Interpolation and definability. Prime and saturated models. Stability. Additional topics. Applications to algebra. Prerequisite: MATH 557.

MATH 565. Foundations of Mathematics II (3) Subsystems of second order arithmetic. Set existence axioms. Reverse mathematics. Foundations of analysis and algebra. Prerequisite: MATH 557 and 558.

MATH 574. Topics in Logic and Foundations (3-6; may be taken repeatedly) Topics in mathematical logic and the foundations of mathematics. Prerequisite: MATH 558.

Sun Apr 19 16:32:27 EDT 1998