Denis R. Hirschfeldt's Papers


Expository Papers

Calibrating randomness (with Rod Downey, André Nies, and Sebastiaan A. Terwijn)

Slicing the truth: on the computability theoretic and reverse mathematical analysis of combinatorial principles


Algorithmic Randomness and Dimension

Randomness, computability, and density (with Rod Downey and André Nies)

Randomness and reducibility (with Rod Downey and Geoff LaForte)

Trivial reals (with Rod Downey, André Nies, and Frank Stephan)

Using random sets as oracles (with André Nies and Frank Stephan)

Relativizing Chaitin's halting probability (with Rod Downey, Joseph S. Miller, and André Nies)

Limit computability and constructive measure (with Sebastiaan A. Terwijn)

Undecidability of the structure of the Solovay degrees of c.e. reals (with Rod Downey and Geoff LaForte)

Characterizing the strongly jump-traceable sets via randomness (with Noam Greenberg and André Nies)

Counting the changes of random Δ02 sets (with Santiago Figueira, Joseph S. Miller, Keng Meng Ng, and André Nies)

Finite self-information (with Rebecca Weber)


Reverse Mathematics and Computable Mathematics

A Delta02 set with no infinite low subset in either it or its complement (with Rod Downey, Steffen Lempp, and Reed Solomon)

Computability-theoretic and proof-theoretic aspects of partial and linear orderings (with Rod Downey, Steffen Lempp, and Reed Solomon)

Reverse mathematics of the Nielsen-Schreier theorem (with Rod Downey, Steffen Lempp, and Reed Solomon)

The strength of some combinatorial principles related to Ramsey's Theorem for pairs (with Carl G. Jockusch, Jr., Bjorn Kjos-Hanssen, Steffen Lempp, and Theodore A. Slaman)

Combinatorial principles weaker than Ramsey's Theorem for pairs (with Richard A. Shore)

Subspaces of computable vector spaces (with Rod Downey, Asher M. Kach, Steffen Lempp, Joseph R. Mileti, and Antonio Montálban)

The Atomic Model Theorem and type omitting (with Richard A. Shore and Theodore A. Slaman)

Induction, bounding, weak combinatorial principles, and the Homogeneous Model Theorem (with Karen Lange and Richard A. Shore)


Computable Model Theory

Degree spectra of intrinsically c.e. relations

Degree spectra of relations on computable structures (doctoral dissertation)

Degree spectra of relations on computable structures (research communication)

Prime models of theories of computable linear orderings

Degree spectra of relations on computable structures in the presence of Delta02 isomorphisms

Degree spectra of relations on structures of finite computable dimension

Degree spectra and computable dimensions in algebraic structures (with Bakhadyr Khoussainov, Richard A. Shore, and Arkadii M. Slinko)

Uniformity in computable structure theory (with Rod Downey and Bakhadyr Khoussainov)

Degree spectra of relations on Boolean algebras (with Rod Downey and Sergey S. Goncharov)

A computably categorical structure whose expansion by a constant has infinite computable dimension (with Bakhadyr Khoussainov and Richard A. Shore)

Realizing levels of the hyperarithmetic hierarchy as degree spectra of relations on computable structures (with Walker M. White)

Bounding prime models (with Barbara F. Csima, Julia F. Knight, and Robert I. Soare)

Computable trees, prime models, and relative decidability

An uncountably categorical theory whose only computably presentable model is saturated (with Bakhadyr Khoussainov and Pavel Semukhin)

Bounding homogeneous models (with Barbara F. Csima, Valentina S. Harizanov, and Robert I. Soare)

Pi01 classes and strong degree spectra of relations (with John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Carl G. Jockusch, Jr., Timothy McNicholl, and Sarah Pingrey)

Order-computable sets (with Russell Miller and Sergei Podzorov)

Categoricity properties for computable algebraic fields (with Ken Kramer, Russell Miller, and Alexandra Shlapentokh)

On finitely presented expansions of computably enumerable semigroups (with Bakhadyr Khoussainov)


Degree Theory

Undecidability and 1-types in intervals of the computably enumerable degrees (with Klaus Ambos-Spies and Richard A. Shore)

Every 1-generic computes a properly 1-generic (with Barbara F. Csima, Rod Downey, Noam Greenberg, and Joseph S. Miller)