Research Interests:  I'm primarily interested in logic and the foundations of mathematics. I received my PhD in August 2003 from Penn State University under the advisorship of Stephen Simpson.  My PhD dissertation and a list of my publications are below.

Curriculum Vitae:  (PDF)

Research Statement(PDF)

2007 Seminar:  Structure and Information

List Of Publications:

Completeness, Compactness, Effective Dimension

(Accepted November 2012 Mathematical Logic Quarterly)

Compressibility and Kolmogorov Complexity

(accepted Jan 2012 Notre Dame Journal of Formal Logic)

Relative Kolmogorov Complexity and Geometry

Journal of Symbolic Logic, Vol 76 Issue 4, (2011)

Finding paths through narrow and wide trees., (with Kjos-Hanssen)

Journal of Symbolic Logic. Volume 74, Issue 1 (2009).

Pi01 classes with complex elements,

Journal of Symbolic Logic. Volume 73, Issue 4 (2008).

Self-embedding of computable trees, (with Kjos-Hanssen, Lerman, Schmerl and Solomon)

Notre Dame Journal of Formal Logic, Volume 49, Number 1, 2008, 1-37.

Hyperimmunity in 2^N,

Notre Dame Journal of Formal Logic, 2007 Volume 48, Number 2, 293-316.

On a conjecture of Dobrinen and Simpson concerning almost everywhere domination, (with Kjos-Hanssen, Lerman and Solomon),

 Journal of Symbolic Logic (Vol 71, March 2006).

Small Pi01 classes,

Archive for Mathematical Logic (Vol 45, May 2006).

Embeddings into the Medevdev and Muchnik lattices of Pi01 classes (with Stephen Simpson),

Archive for Mathematical Logic, Vol 43, Number 3, April 2004.

A Splitting Theorem for the Medvedev and Muchnik Lattices 

 Mathematical Logic Quarterly, Vol 49, Issue 4, May 2003.

Dissertation: The Pennsylvania State University (2003)

The Medvedev and Muchnik lattices of Pi01 classes 

Project (Completed)

Algorithmic Complexity and Effectively Closed Classes




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