5 papers
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…
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…