dzhafarov

Damir Dzhalil Dzhafarov

Visiting Assistant Professor

Ph.D., University of Chicago, 2011
M.S., University of Chicago, 2006
B.Sc., Purdue University, 2005

Email:  ddzhafar "at" nd.edu

Office:  214 Hayes-Healy Hall
Phone:  (574) 631-6288
Fax:  (574) 631-6579

For additional information see Damir Dzhafarov's Personal Page.

Research Interests

I study the logical strength of mathematical theorems using the tools of computability theory and reverse mathematics. This type of research deepens our insight into the fundamental properties of the constructions needed to prove a given class of theorems, and exposes connections between theorems from different fields. A surprising fact repeatedly demonstrated in this area over the last few decades is that a vast number of mathematical theorems can be classified into just five main types. This points to a great deal of regularity underlying many of the arguments mathematicians employ. I am particularly interested in the strength of theorems that fall outside of this classification, and whose logical content is therefore more difficult to describe. Examples of these include combinatorial principles related to Ramsey's theorem, the atomic model theorem, and various equivalents of the axiom of choice. My current research is focused on identifying further examples of theorems of this kind, especially from other branches of mathematics, and understanding the global structure of how they relate to each other.

Selected Publications

  • Reverse mathematics and equivalents of the axiom of choice (with C. Mummert), submitted 
  • Infinite saturated orders, Order, 28 (2011), no. 2, 163–172.
  • Stable Ramsey’s theorem and measure, Notre Dame Journal of Formal Logic, 52 (2011), no. 1, 95–112
  • Ramsey’s theorem and cone avoidance (with C. G. Jockusch, Jr.), Journal of Symbolic Logic, 74 (2009), no. 2, 557–578
  • Definitions of finiteness based on order properties (with O. De la Cruz and E. J. Hall), Fundamenta Mathematicae, 189 (2006), no. 2, 155–172


Please direct questions and comments to:  ddzhafar "at" nd.edu