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Proof-theoretic strength of the stable marriage theorem and other problems

Published online by Cambridge University Press:  31 March 2017

By
Douglas Cenzer  and
Jeffrey B. Remmel
Edited by
Stephen G. Simpson
Stephen G. Simpson
Affiliation:
Pennsylvania State University
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Type
Chapter
Information
Reverse Mathematics 2001 , pp. 67 - 103
Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] Ron, Aharoni, Menachem, Magidor, and Richard A., Shore, On the strength of König's duality theorem for infinite bipartite graphs,Journal of Combinatorial Theory. Series B, vol. 54 (1992), no. 2, pp. 257–290.
[2] Peter G., Clote and Jeffry L., Hirst, Reverse mathematics of some topics from algorithmic graph theory,Fundamenta Mathematicae, vol. 157 (1998), no. 1, pp. 1–13.
[3] R. P., Dilworth, A decomposition theorem for partially ordered sets,Annals ofMathematics. Second Series, vol. 51 (1950), pp. 161–166.
[4] Ben, Dushnik and E.W., Miller, Partially ordered sets,American Journal ofMathematics, vol. 63 (1941), pp. 600–610.
[5] D., Gale and L., Shapley, College admissions and the stability of marriage,American Mathematical Monthly, vol. 69 (1962), pp. 9–15.
[6] William, Gasarch and Jeffry L., Hirst, Reverse mathematics and recursive graph theory,MLQ. Mathematical Logic Quarterly, vol. 44 (1998), no. 4, pp. 465–473.
[7] J., Hirst, Combinatorics in subsystems of second order arithmetic, Ph.D. thesis, Pennsylvania State University, 1987.
[8] Jeffry L., Hirst, Marriage theorems and reverse mathematics,Logic and computation (Pittsburgh, PA, 1987), Contemp. Math., vol. 106, Amer. Math. Soc., Providence, RI, 1990, pp. 181–196.
[9] Jeffry L., Hirst, Reverse mathematics and rank functions for directed graphs,Archive for Mathematical Logic, vol. 39 (2000), no. 8, pp. 569–579.
[10] Jeffry L., Hirst, Reverse mathematics and rank functions for directed graphs,Archive for Mathematical Logic, vol. 39 (2000), no. 8, pp. 569–579.
[11] H. A., Kierstead, Recursive and on-line graph coloring,Handbook of recursive mathematics, vol. 2(Y., Ersov, S., Goncharov, A., Nerode, and J., Remmel, editors), Stud. Logic Found. Math., vol. 139, North-Holland, Amsterdam, 1998, pp. 1233–1269.
[12] Henry A., Kierstead, An effective version of Dilworth's theorem,Transactions of the American Mathematical Society, vol. 268 (1981), no. 1, pp. 63–77.
[13] Henry A., Kierstead, George F., McNulty, and William T., Trotter, Jr., Recursive dimension for partially ordered sets,Order, vol. 1 (1984), no. 1, pp. 67–82.
[14] Donald E., Knuth, Stable marriage and its relation to other combinatorial problems, CRM Proceedings & Lecture Notes, vol. 10, American Mathematical Society, Providence, RI, 1997.
[15] J. B., Remmel, Graph colorings and recursively bounded Π0/1 -classes,Annals of Pure and Applied Logic, vol. 32 (1986), no. 2, pp. 185–194.
[16] Stephen G., Simpson, On the strength of König's duality theorem for countable bipartite graphs,The Journal of Symbolic Logic, vol. 59 (1994), no. 1, pp. 113–123.
[17] Stephen G., Simpson, Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.

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