# 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 | 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 |

Clifton F. Ealy | Visiting Associate Professor | Model theory, independence relations |

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 |
---|---|---|

Takayuki Kihara | Postdoc | Computability theory, descriptive set theory |

Ludovic Patey | Morrey Visiting Assistant Professor | Computability theory, reverse mathematics |

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 |

## Graduate Students

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

Reid Dale | |

Daniel Fremont | |

Matthew Harrison-Trainor | Antonio Montalbán |

Alexander Kocurek | |

James Gardner Moody | |

Nick Ramsey | |

Mariana Vicaria | |

James Walsh | |

Michael Wan | Thomas Scanlon |

Kentarô Yamamoto |

## 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 |