Reverse Mathematics of Matroids

  title={Reverse Mathematics of Matroids},
  author={Jeffry L. Hirst and Carl Mummert},
  booktitle={Computability and Complexity},
  • Jeffry L. Hirst, Carl Mummert
  • Published in Computability and Complexity 2017
  • Mathematics, Computer Science
  • 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 of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles and statements about vector spaces. Finally, we formalize some of the Weihrauch reductions to extract… CONTINUE READING
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