# 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 |

## Graduate Students

Name | Dissertation Supervisor |
---|---|

Diego Andres Bejarano Rayo | Thomas Warren Scanlon |

Katalin Berlow | |

Jordan Brown | |

Alex Burka | |

Matthew Duvalier | Ted Slaman |

David Gonzalez | |

Daniel Gonzalez | |

Zakkai Goriely | |

Guillaume Massas | Wes Holliday, Paolo Mancosu |

Ronan O'Gorman | |

Jacob Parish | |

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 |