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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
Gabriel Goldberg Assistant Professor Set theory, large cardinals, inner model theory, infinite combinatorics
Leo Anthony Harrington Professor Emeritus Recursion theory, Model theory, Set theory
Andrew Marks Professor Descriptive set theory and connections with computability, combinatorics, ergodic theory, operator algebras
Ralph McKenzie Professor Emeritus General algebra, Logic
Antonio Montalbán Professor Mathematical logic, computability theory
Thomas Scanlon Professor Model theory and applications to number theory
Theodore A. Slaman Professor Emeritus 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
C. Ward Henson Visitor Continuous logic and model theory of metric structures; nonstandard analysis
Eudes Naziazeno Galvão Visiting Scholar Model theory
Dana Scott Visitor Foundations of logic and mathematics, semantics of programming languages
Carol Wood Visitor Model theory and its interactions with algebra and combinatorics

Postdocs

Name Title Research Interests
Eyal Kaplan Postdoctoral Scholar Set theory, forcing, large cardinals
Forte Shinko Postdoctoral Scholar Descriptive set theory, topological and measurable dynamics, geometric group theory

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
Reid RG Dale Logical Interrogations of Theory and Evidence   Thomas Scanlon, Wesley Holliday 2022
Adele Padgett Sublogarithmic-Transexponential Series   Thomas Scanlon 2022
Patrick Lutz Results on Martin's Conjecture   Ted Slaman 2021
James Walsh Reflection Principles and Ordinal Analysis Antonio Montalbán 2020
Kentarô Yamamoto Duality for boolean algebra expansions and its applications 2020
Daniel Fremont Algorithmic Improvisation Sanjit Seshia 2019
James Gardner Moody Computable Continuous Structure Theory Antonio Montalban, Theodore Slaman 2019
Alexander Kocurek What Can You Say? Measuring the Expressive Power of Languages   Wesley Holliday, Seth Yalcin 2018
Nick Ramsey Independence, Amalgamation, and Trees   Tom Scanlon 2018
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