18 citations · 65 across the 11 of their papers we have counts for
13 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…
The logical strength of König's edge coloring theorem
Carl Mummert
König's edge coloring theorem says that a bipartite graph with maximal degree has an edge coloring with no more than colors. We explore the computability theory and Reverse…
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 Erasure Combinatorial Batch Codes
JiYoon Jung, Carl Mummert, Elizabeth Niese +1
Combinatorial batch codes were defined by Paterson, Stinson, and Wei as purely combinatorial versions of the batch codes introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai. The…
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…