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Next: 5 Graduate course offerings Up: 4 Graduate course offerings Previous: 4.1 Undergraduate/Graduate (400) Level

4.2 Graduate Level (500) Courses (logic only)

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.

Stephen G Simpson
Sun Apr 19 16:32:27 EDT 1998