guingona180

Vincent Guingona

Visiting Assistant Professor

B.S., University of Chicago, 2005
Ph.D., University of Maryland, 2011

Email:  guingona (dot) 1 (at) nd (dot) edu
Office:  118 Hayes-Healy Hall
Phone:  (574) 631-6505

For additional information see Vincent Guingona's Personal Page.

Research Interests: 

My research interests are in a branch of logic called model theory.  Specifically, I am interested in generalizing notions from classification theory to dependent theories.  The primary notion I have been interested in recently is definability of types.

In my graduate thesis, I provide a candidate for definability of types in dependent theories: uniform definability of types over finite sets (UDTFS).  Much of my recent research is aimed at understanding UDTFS and related notions and finding applications to other areas of model theory.  My main goal is to show that UDTFS is equivalent to dependence.  As a partial answer to this, I have shown that various subclasses of the class of dependent theories have UDTFS, including dp-minimal theories.  As an example of an application of UDTFS, counting the number of parameters needed in the UDTFS definition of a formula gives a bound on the VC-density of that formula.

I am also interested in understanding "low-rank" dependent theories, such as VC-minimal and dp-minimal theories.  How do standard model-theoretic notions behave in these theories?  How are various notions of rank, such as VC-dimension, VC-density, and dp-rank, related?

Publications:

  • Dependence and isolated extensions. Proc. Amer. Math. Soc. 139 (2011), 3349-3357
  • On uniform definability of types over finite sets. J. Symbolic Logic (to appear).
  • Definability of types over finite partial order indiscernibles. submitted, 10 August 2011.
  • Local dp-rank and VC-density over indiscernible sequences. submitted, 11 August 2011 (joint with Cameron Donnay Hill).


Please direct questions and comments to :  guingona (dot) 1 (at) nd (dot) edu