MATH225A
Overview
Subject: Math
Course Number: 225A
Department: Mathematics
Course Level: Graduate
Course Title
Metamathematics
Course Description
Metamathematics of predicate logic. Completeness and compactness theorems. Interpolation theorem,definability,theory of models. Metamathematics of number theory, recursive functions, applications to truth and provability. Undecidable theories. Sequence begins fall.
Units
Minimum Units: 4
Maximum Units: 4
Prior Terms Offered
MATH225B
Overview
Subject: Math
Course Number: 225B
Department: Mathematics
Course Level: Graduate
Course Title
Metamathematics
Course Description
Metamathematics of predicate logic. Completeness and compactness theorems. Interpolation theorem, definability, theory of models. Metamathematics of number theory, recursive functions, applications to truth and provability. Undecidable theories. Sequence begins fall.
Units
Minimum Units: 4
Maximum Units: 4
Prior Terms Offered
MATH227A
Overview
Subject: Math
Course Number: 227A
Department: Mathematics
Course Level: Graduate
Course Title
Theory of Recursive Functions
Course Description
Recursive and recursively enumerable sets of natural numbers; characterizations, significance, and classification. Relativization, degrees of unsolvability. The recursion theorem. Constructive ordinals, the hyperarithmetical and analytical hierarchies. Recursive objects of higher type. Sequence begins fall.
Units
Minimum Units: 4
Maximum Units: 4
Prior Terms Offered
MATH229
Overview
Subject: Math
Course Number: 229
Department: Mathematics
Course Level: Graduate
Course Title
Theory of Models
Course Description
Syntactical characterization of classes closed under algebraic operations. Ultraproducts and ultralimits, saturated models. Methods for establishing decidability and completeness. Model theory of various languages richer than first-order.
Units
Minimum Units: 4
Maximum Units: 4
Prior Terms Offered
MATH235A
Overview
Subject: Math
Course Number: 235A
Department: Mathematics
Course Level: Graduate
Course Title
Theory of Sets
Course Description
Axiomatic foundations. Operations on sets and relations. Images and set functions. Ordering, well-ordering, and well-founded relations; general principles of induction and recursion. Ranks of sets, ordinals and their arithmetic. Set-theoretical equivalence, similarity of relations; definitions by abstraction. Arithmetic of cardinals. Axiom of choice, equivalent forms, and consequences. Sequence begins fall.
Units
Minimum Units: 4
Maximum Units: 4
Prior Terms Offered
MATH236
Overview
Subject: Math
Course Number: 236
Department: Mathematics
Course Level: Graduate
Course Title
Metamathematics of Set Theory
Course Description
Various set theories: comparison of strength, transitive, and natural models, finite axiomatizability. Independence and consistency of axiom of choice, continuum hypothesis, etc. The measure problem and axioms of strong infinity.
Minimum Units: 4
Maximum Units: 4