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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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