Research in Mathematical Logic

Including model theory, recursion theory, and set theory

We have a large active group of researchers in several core areas of mathematical logic, including model theory, recursion theory and set theory. A number of members of the logic group belong to the Group in Logic and Methodology of Science, which runs a bi-weekly colloquium and has its own graduate students.

Courses

Undergraduate upper division courses

Math 125A. Mathematical logic.
Math 135. Set theory.
Math 136. Incompleteness and Undecidability.

Graduate courses

Math 225A-225B. Metamathematics.
Math 227A. Theory of recursive functions.
Math 229. Theory of models.
Math 235A. Theory of sets.
Math 236. Metamathematics of Set Theory.

Seminars

2009-2010

Math 290. Recursion Theory, Leo Harrington and Theodore Slaman
Math 290. Model Theory, Tom Scanlon
Math 290. Inner Model Theory, John Steel

Senate Faculty

Name Title Research Interests
John W. Addison Jr. Professor Emeritus Theory of definability, Descriptive set theory, Model theory, Recursive function theory
Leo Anthony Harrington Professor Emeritus Recursion theory, Model theory, Set theory
Ralph McKenzie Professor Emeritus General algebra, Logic
Antonio Montalbán Associate Professor Mathematical logic, computability theory
Thomas Scanlon Professor Model theory and applications to number theory
Pierre Simon Assistant Professor Model theory
Theodore A. Slaman Professor Recursion theory, mathematical logic
Robert M. Solovay Professor Emeritus Mathematical Logic
John R. Steel Professor Emeritus Set theory, Descriptive set theory, Fine structure
W. Hugh Woodin Professor Emeritus Set theory, Large cardinals, Mathematical logic

Visiting Faculty

Name Title Research Interests
Martin Davis Visiting Scholar Logic, diophantine decision problems
C. Ward Henson Visiting Scholar Continuous logic and model theory of metric structures; nonstandard analysis
Jung-Uk Lee Visiting Scholar Model theory; arithmetic of nonstandard rational number fields, model theory of valued fields, abstract independence relations
Dana Scott Visiting Scholar Foundations of logic and mathematics, semantics of programming languages
Carol Wood Visiting Scholar Model theory and its interactions with algebra and combinatorics

Postdocs

Name Title Research Interests
Silvain Rideau Morrey Visiting Assistant Professor Model theory, valued fields

Faculty with Related Research Interests

Name Title Research Interests
George M. Bergman Professor Emeritus, Professor of the Graduate School Associative rings, Universal algebra and category theory, Counterexamples

Recent Ph.D.s

Name Dissertation Title Dissertation Supervisor Year
Will Johnson Fun with Fields 2016
Alex Kruckman Infinitary Limits of Finite Structures Thomas Scanlon 2016
Lawrence Valby 2015
Kelty Allen Martin-Löf Randomness and Brownian Motion Theodore A. Slaman 2014
Ian R. Haken Randomizing Reals and the First-Order Consequences of Randoms Theodore A. Slaman 2014
Gwyneth Harrison-Shermoen Independence Relations in Theories with the Tree Property Thomas Scanlon 2014
Arthur Tilley Thomas Scanlon 2014
Linda Westrick Computability in Ordinal Ranks and Symbolic Dynamics Theodore A. Slaman 2014
Julia Erhard The Carlson-Simpson Lemma in Reverse Mathematics Theodore A. Slaman 2013
Ian Herbert Weak Lowness Notions for Kolmogorov Complexity Theodore A. Slaman 2013
Gregory Igusa Generic Reduction, and Work with Partial Computations and Partial Oracles Theodore A. Slaman 2013
Andrew Marks Recursion Theory and Countable Borel Equivalence Relations Theodore A. Slaman 2012
Trevor Wilson Contributions to DescriptiveInner Model Theory John R. Steel 2012
Alex Rennet Ultraproducts of O-Minimal Structures Thomas Scanlon