Mathematical Logic
A year-long introduction to model theory, proof theory and incompleteness, computability, and set theory. This is the standard first-year sequence for graduate students in logic.
UCLA Logic Center
Information for Students
Paths into mathematical logic at UCLA from undergraduate studies to graduate research.
Study Logic at UCLA
Prospective graduate students interested in mathematical logic should apply through the UCLA Department of Mathematics and identify logic as a field of interest in the application. No separate application or materials need to be sent to the Logic Center.
Logic students normally take the year-long Math 220ABC sequence in their first year. It develops the foundations of model theory, proof theory, computability theory, and set theory and prepares students for the logic qualifying examination. After the qualifying exams, students typically arrange reading courses with faculty as they move toward dissertation research.
Students are also encouraged to attend the Logic Colloquium and Logic Seminar, where they can encounter current research across the field.
Graduate Courses
The core sequence is complemented by rotating advanced topics and research seminars. Consult the live schedule to see which courses are offered in a particular quarter.
Topics in Computability Theory
Advanced topics in recursion and computability theory; the precise subject varies by offering.
Topics in Descriptive Set Theory
Topics vary and may include Borel and projective sets, infinite games, determinacy, structural and effective questions, and applications of descriptive set theory.
Topics in Model Theory
Rotating advanced topics in model theory and its interactions with algebra, geometry, analysis, and combinatorics.
Topics in Set Theory
Advanced set theory, with topics that may include forcing, large cardinals, determinacy, inner models, and cardinal combinatorics.
Seminars and participating seminars
Variable-topic seminars in current logic research, often organized around faculty or visitor expertise.
Courses in Other Departments
Logic at UCLA extends beyond Mathematics. Relevant offerings vary by year, so students should verify prerequisites and current availability with the department concerned.
Logic, semantics, and philosophy of science
The Philosophy Department groups its graduate offerings in logic, semantics, philosophy of mathematics, and philosophy of science in this range.
Topics in Set Theory
Sets and orderings, ordinal and cardinal arithmetic, formal set theories, and foundational questions.
Topics in Mathematical Logic
A variable-topic graduate course whose content reflects current work in mathematical and philosophical logic.
Semantic Theory I–II
The graduate semantics sequence, developing formal approaches to linguistic meaning and the syntax–semantics interface.
Computer-Aided Verification
Formal methods for hardware and software systems, including temporal logic, model checking, invariants, automata, and compositional reasoning.
Undergraduate Courses
These courses offer useful preparation for advanced work in mathematical logic. The linked catalog descriptions give the current prerequisites and grading rules.
Introduction to Discrete Structures
Sets and relations, induction, combinatorics, graphs, and trees: the basic language of discrete mathematics.
Computability Theory
Turing computability, recursive and recursively enumerable sets, undecidability, relative computability, and the arithmetical hierarchy.
Mathematical Logic
Formal deduction, completeness, compactness, Löwenheim–Skolem theorems, nonstandard models, and Gödel incompleteness.
Philosophy M134
Introduction to Set Theory
Axiomatic set theory as a foundation for mathematics, including relations and functions, cardinality, the Axiom of Choice, and transfinite numbers.
Logic, First Course
An introduction to sentential and quantificational logic, designed in part for students planning further study in logic.
Introduction to Metalogic
Formal languages, deductive systems and models, with compactness and completeness at the center.
Modal Logic
Model theory for logics of possibility, necessity, time, knowledge, and action.
Computational Linguistics I–II
Formal computational ideas underlying linguistic grammars, including recursion, parsing algorithms, probabilities and grammars, and computational analysis of linguistic frameworks.
Theory of Computing
Finite-state machines, formal languages, automata, Turing machines, undecidability, and an introduction to computability.
Logic Qualifying Exams
The logic area examination covers computability theory, model theory, set theory, and incompleteness. Math 220ABC provides the principal preparation, while the department’s syllabus gives a detailed outline of expected material and references.