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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)
2007 Seminar: Structure and Information
List Of Publications:
Finding paths through narrow and wide trees.
, (with Kjos-Hanssen)(submitted March 2008).
Pi01 classes with complex elements,
(submitted Sept 2007, Journal of Symbolic Logic, to appear).
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.
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). 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 (under review)
Algorithmic Complexity and Effectively Closed Classes