43 citations · 55 across the 12 of their papers we have counts for
15 papers
Thin Set Versions of Hindman's Theorem
Denis R. Hirschfeldt, Sarah C. Reitzes
In this paper we examine the reverse mathematical strength of a variation of Hindman's Theorem HT constructed by essentially combining HT with the Thin Set Theorem TS to obtain a p…
A Feiner Look at the Intermediate Degrees
Denis R. Hirschfeldt, Asher M. Kach, Antonio Montalbán
We say that a set is if membership of in is a question, uniformly in . A set is low for -Feiner if every set that is $Δ^0_{(n)…
Coarse computability, the density metric, Hausdorff distances between Turing degrees, perfect trees, and reverse mathematics
Denis R. Hirschfeldt, Carl G. Jockusch, Paul E. Schupp
The coarse similarity class of is the set of all whose symmetric difference with has asymptotic density 0. There is a natural metric on the space $\mathcal{S}…
Reduction games, provability, and compactness
Damir D. Dzhafarov, Denis R. Hirschfeldt, Sarah C. Reitzes
Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications betwe…
A minimal pair in the generic degrees
Denis R. Hirschfeldt
We show that there is a minimal pair in the nonuniform generic degrees, and hence also in the uniform generic degrees. This fact contrasts with Igusa's result that there are no min…
Some results concerning the vs. problem
Peter A. Cholak, Damir D. Dzhafarov, Denis R. Hirschfeldt +1
The vs.\ problem is a central problem in computable combinatorics and reverse mathematics, asking whether every Turing ideal that satisfies the pr…
Combinatorial principles equivalent to weak induction
Caleb Davis, Denis R. Hirschfeldt, Jeffry L. Hirst +3
We consider two combinatorial principles, and . Both are easily proved in plus induction. We give two proofs of in ${…
Dense computability, upper cones, and minimal pairs
Eric P. Astor, Denis R. Hirschfeldt, Carl G. Jockusch
This paper concerns algorithms that give correct answers with (asymptotic) density . A dense description of a function is a partial function on such that $\…
The reverse mathematics of Hindman's theorem for sums of exactly two elements
Barbara F. Csima, Damir D. Dzhafarov, Denis R. Hirschfeldt +3
Hindman's Theorem (HT) states that for every coloring of with finitely many colors, there is an infinite set such that all nonempty sums of dist…
Ramsey's theorem and products in the Weihrauch degrees
Damir D. Dzhafarov, Jun Le Goh, Denis R. Hirschfeldt +2
We study the positions in the Weihrauch lattice of parallel products of various combinatorial principles related to Ramsey's theorem. Among other results, we obtain an answer to a…
Asymptotic density and the coarse computability bound
Denis R. Hirschfeldt, Carl G. Jockusch, Timothy H. McNicholl +1
For we say that a set is \emph{coarsely computable at density} if there is a computable set such that has lower density…
Coarse Reducibility and Algorithmic Randomness
Denis R. Hirschfeldt, Carl G. Jockusch, Rutger Kuyper +1
A coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputabl…
The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs
Denis R. Hirschfeldt, Carl G. Jockusch, Bjørn Kjos-Hanssen +2
We study the reverse mathematics and computability-the\-o\-re\-tic strength of (stable) Ramsey's Theorem for pairs and the related principles COH and DNR. We show that SRT im…
Categoricity Properties for Computable Algebraic Fields
Denis Hirschfeldt, Ken Kramer, Russell Miller +1
We examine categoricity issues for computable algebraic fields. We give a structural criterion for relative computable categoricity of these fields, and use it to construct a field…
Characterizing the strongly jump-traceable sets via randomness
Noam Greenberg, Denis Hirschfeldt, Andre Nies
We show that if a set is computable from every superlow 1-random set, then is strongly jump-traceable. This theorem shows that the computably enumerable (c.e.) strongly jum…