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 | Professor Emeritus | Theory of definability, Descriptive set theory, Model theory, Recursive function theory |
| Leo A. Harrington | Professor | 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 |
| Jack H. Silver | Professor Emeritus | Mathematical logic, Theory of sets |
| Theodore A. Slaman | Professor | Recursion theory, mathematical logic |
| Robert M. Solovay | Professor Emeritus | Mathematical Logic |
| John R. Steel | Professor | Set theory, Descriptive set theory, Fine structure |
| W. Hugh Woodin | Professor | Set theory, Large cardinals, Mathematical logic |
Visiting Faculty
| Name | Title | Research Interests |
|---|---|---|
| Martin Davis | Visiting Scholar | Logic, diophantine decision problems |
| Itay Neeman | Visiting Scholar | Set theory, large cardinals, forcing |
| Farmer Schlutzenberg | Visiting Scholar | |
| Dana Scott | Visiting Scholar | Foundations of logic and mathematics, semantics of programming languages |
| Mariya Soskova | Visiting Scholar | Mathematical logic and computability |
Postdocs
| Name | Title | Research Interests |
|---|---|---|
| Adam Day | Miller Research Fellow | Algorithmic Information Theory and Randomness |
| James Freitag | NSF Postdoctoral Fellow | Model theory, differential algebra, algebraic geometry |
| Daisuke Ikegami | Postdoctoral Fellow | Set Theory |
| Alice Medvedev | FRG Postdoctoral Fellow | Model Theory, Algebraic Dynamics |
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 |
|---|---|
| Kelty Allen | Theodore A. Slaman |
| Richard Dore | W. Hugh Woodin |
| Julia Erhard | Theodore A. Slaman |
| Ian R. Haken | Theodore A. Slaman |
| Gwyneth Harrison-Shermoen | Thomas Scanlon |
| Ian Herbert | Theodore A. Slaman |
| Gregory Igusa | Theodore A. Slaman |
| Alex Kruckman | Thomas Scanlon |
| Adam Lesnikowski | |
| Lisha (Janet Xiang) Li | |
| Dominic McCarty | W. Hugh Woodin |
| Shahin Saadati | |
| Arthur Tilley | Thomas Scanlon |
| Lawrence Valby | |
| Michael Wan | |
| Linda Westrick | Theodore A. Slaman |
Recent Ph.D.s
| Name | Dissertation Title | Dissertation Supervisor | Year |
|---|---|---|---|
| Andrew Marks | Recursion Theory and CountableBorel Equlivalence Relations | Theodore A. Slaman | 2012 |
| Meghan Anderson | Solution Spaces for Linear Equations in Valued D-Fields | Thomas Scanlon | 2011 |
| Koushik Pal | Uniform Theory of Multiplicative Valued Difference Fields | Thomas Scanlon | 2011 |
| Uri Andrews | Amalgamation Constuction and Recursive Model Theory | Thomas Scanlon | 2010 |
| Cameron Donnay Hill | Geometric Model Theory in Efficient Computability | Leo A Harrington | 2010 |
| Lynn Cho Scow | Characterization Theorems by Genearlized Indiscernibles | Thomas Scanlon | 2010 |
| Charles Smart | On the Infinity Laplacian and Hrushouski's Fusion | Craig Evans, Leo Harrington | 2010 |
| Paul Baginski | Stable aleph-naught catergorical Algebraic Structures | Thomas Scanlon | 2009 |
| Erik William Closson | The Solovay Sequence in Derived Models Associated to Mice | John Steel | 2008 |
| Joseph Flenner | The Relative Structure of Henselian Valued Fields | Thomas Scanlon | 2008 |
| Janak Ramakrishnan | Types in o-minimal theories | Thomas Scanlon | 2008 |
