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, starting Summer 2023 | Descriptive set theory |
| Ralph McKenzie | Professor Emeritus | General algebra, Logic |
| Antonio Montalbán | Professor | Mathematical logic, computability theory |
| Thomas Scanlon | Professor | Model theory and applications to number theory |
| Pierre Simon | Associate 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 |
|---|---|---|
| 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 |
|---|---|---|
| Sebastian Eterović | RTG Postdoctoral Scholar & Unit 18 Lecturer | Arithmetic geometry, model theory |
| Dino Rossegger | Postdoctoral Scholar | Computability 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 |
Graduate Students
| Name | Dissertation Supervisor |
|---|---|
| Diego Andres Bejarano Rayo | Thomas Warren Scanlon |
| Katalin Berlow | |
| Jordan Brown | |
| Alex Burka | |
| Matthew Duvalier | Ted Slaman |
| David Gonzalez | |
| Guillaume Massas | Wes Holliday, Paolo Mancosu |
| Ronan O'Gorman | |
| Shoshana Simons | |
| Yuki Takahashi | |
| Mariana Vicaria | Thomas Scanlon, Pierre Simon |
| Harper Wells | |
| Rebecca Whitman |
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 |
