3 papers
math.LO2020
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…
math.LO2016
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…
math.LO2010
Reverse mathematics and equivalents of the axiom of choice
Damir D. Dzhafarov, Carl Mummert
We study the reverse mathematics of countable analogues of several maximality principles that are equivalent to the axiom of choice in set theory. Among these are the principle ass…