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Free sets and reversemathematics

Published online by Cambridge University Press:  31 March 2017

Stephen G. Simpson
Affiliation:
Pennsylvania State University
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Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] Peter A., Cholak, Carl G., Jockusch, and Theodore A., Slaman, On the strength of Ramsey's theorem for pairs,The Journal of Symbolic Logic, vol. 66 (2001), no. 1, pp. 1–55.
[2] Keith J., Devlin, Some weak versions of large cardinal axioms,Annals of Mathematical Logic, vol. 5 (1972–1973), pp. 291–325.
[3] Keith J., Devlin and Jeff B., Paris, More on the free subset problem,Annals ofMathematical Logic, vol. 5 (1972–1973), pp. 327–336.
[4] Randall L., Dougherty, Narrow coverings of ω-ary product spaces,Annals of Pure and Applied Logic, vol. 88 (1997), no. 1, pp. 47–91.
[5] Harvey M., Friedman, private communication.
[6] Harvey M., Friedman, Fom:53:Free sets and reverse math and Fom:54:Recursion theory and dynamics, at http://www.math.psu.edu/simpson/fom/.
[7] Harvey M., Friedman and Stephen G., Simpson, Issues and problems in reversemathematics,Computability theory and its applications (Boulder, CO, 1999), Contemp.Math., vol. 257, Amer. Math. Soc., Providence, RI, 2000, pp. 127–144.
[8] Jeffry L., Hirst, Combinatorics in subsystems of second order arithmetic, Ph.D. thesis, The Pennsylvania State University, 1987.
[9] Tamara J., Hummel and Carl G., Jockusch, Jr., Ramsey's theorem for computably enumerable colorings,The Journal of Symbolic Logic, vol. 66 (2001), no. 2, pp. 873–880.
[10] Carl G., Jockusch, Jr., Ramsey's theorem and recursion theory,The Journal of Symbolic Logic, vol. 37 (1972), pp. 268–280.
[11] Carl G., Jockusch, Upward closure and cohesive degrees,Israel Journal of Mathematics, vol. 15 (1973), pp. 332–335.
[12] Julia F., Knight, Algebraic independence,The Journal of Symbolic Logic, vol. 46 (1981), no. 2, pp. 377–384.
[13] Keith R., Milliken, Ramsey's theorem with sums or unions,Journal of Combinatorial Theory. Series A, vol. 18 (1975), pp. 276–290.
[14] David, Seetapun and Theodore A., Slaman, On the strength of Ramsey's theorem,Notre Dame Journal of Formal Logic, vol. 36 (1995), no. 4, pp. 570–582, Special Issue: Models of arithmetic.
[15] Stephen G., Simpson, Subsystems of second order arithmetic, Perspectives inMathematical Logic, Springer-Verlag, Berlin, 1999.

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