18 citations · 34 across the 12 of their papers we have counts for
16 papers
Banach's theorem in higher order reverse mathematics
Jeffry L. Hirst, Carl Mummert
In this paper, methods of second order and higher order reverse mathematics are applied to versions of a theorem of Banach that extends the Schroeder-Bernstein theorem. Some additi…
Reverse mathematics and Weihrauch analysis motivated by finite complexity theory
Zack BeMent, Jeffry Hirst, Asuka Wallace
We extend a study by Lempp and Hirst of infinite versions of some problems from finite complexity theory, using an intuitionistic version of reverse mathematics and techniques of W…
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 ${…
Leaf management
Jeffry L. Hirst
Finding the set of leaves for an unbounded tree is a nontrivial process in both the Weihrauch and reverse mathematics settings. Despite this, many combinatorial principles for tree…
Reverse mathematics and colorings of hypergraphs
Caleb Davis, Jeffry Hirst, Jake Pardo +1
Working in subsystems of second order arithmetic, we formulate several representations for hypergraphs. We then prove the equivalence of various vertex coloring theorems to ${\sf W…
Using Ramsey's Theorem Once
Jeffry L. Hirst, Carl Mummert
We show that RT(2,4) cannot be proved with one typical application of RT(2,2) in an intuitionistic extension of RCA0 to higher types, but that this does not remain true when the la…
Reverse Mathematics of Matroids
Jeffry L. Hirst, Carl Mummert
Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques…
On the existence of a connected component of a graph
Kirill Gura, Jeffry L. Hirst, Carl Mummert
We study the reverse mathematics and computability of countable graph theory, obtaining the following results. The principle that every countable graph has a connected component is…
Comparing the strength of diagonally non-recursive functions in the absence of induction
François G. Dorais, Jeffry L. Hirst, Paul Shafer
We prove that the statement "there is a such that for every there is a -bounded diagonally non-recursive function relative to " does not imply weak König's lemma over…
On uniform relationships between combinatorial problems
François G. Dorais, Damir D. Dzhafarov, Jeffry L. Hirst +2
The enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic. In this setting, called reverse mathematics, one inve…
Reverse Mathematics and Algebraic Field Extensions
François G. Dorais, Jeffry Hirst, Paul Shafer
This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section 2, we show that is equivalent to the ability…
On Mathias generic sets
Peter A. Cholak, Damir D. Dzhafarov, Jeffry L. Hirst
We present some results about generics for computable Mathias forcing. The -generics and weak -generics in this setting form a strict hierarchy as in the case of Cohen forcin…
Reverse mathematics and uniformity in proofs without excluded middle
Jeffry L. Hirst, Carl Mummert
We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak…
Partitions of trees and ACA'
Bernard A. Anderson, Jeffry L. Hirst
We show that a version of Ramsey's theorem for trees for arbitrary exponents is equivalent to the subsystem ACA' of reverse mathematics.
Infinite versions of some NP-complete problems
Jeffry L. Hirst, Steffen Lempp
Recently, connections have been explored between the complexity of finite problems in graph theory and the complexity of their infinite counterparts. As is shown in our paper (and…
Reverse Mathematics and Recursive Graph Theory
William Gasarch, Jeffry Hirst
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theore…