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Reverse mathematics and marriage problems with finitely many solutions

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Abstract

We analyze the logical strength of theorems on marriage problems with a fixed finite number of solutions via the techniques of reverse mathematics. We show that if a marriage problem has k solutions, then there is a finite set of boys such that the marriage problem restricted to this set has exactly k solutions, each of which extend uniquely to a solution of the original marriage problem. The strength of this assertion depends on whether or not the marriage problem has a bounding function. We also answer three questions from our previous work on marriage problems with unique solutions.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Appalachian State University, Boone, NC, USA

    Jeffry L. Hirst

  2. Department of Mathematics, University of Connecticut, Storrs, CT, USA

    Noah A. Hughes

Authors
  1. Jeffry L. Hirst
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  2. Noah A. Hughes
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Correspondence to Jeffry L. Hirst.

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Hirst, J.L., Hughes, N.A. Reverse mathematics and marriage problems with finitely many solutions. Arch. Math. Logic 55, 1015–1024 (2016). https://doi.org/10.1007/s00153-016-0509-4

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  • DOI: https://doi.org/10.1007/s00153-016-0509-4

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