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Reversemathematics and ordinal suprema

Published online by Cambridge University Press:  31 March 2017

By
Jeffry L. Hirst
Edited by
Stephen G. Simpson
Stephen G. Simpson
Affiliation:
Pennsylvania State University
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Reverse Mathematics 2001 , pp. 235 - 243
Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] Georg, Cantor, Beiträge zur Begründung der transfinitenMengenlehre, Mathematische Annalen., vol. 49 (1897), pp. 207–246, English translation by P., Jourdain published as Contributions to the founding of the theory of transfinite numbers, Dover, New York, 1955.
[2] Harvey M., Friedman, Systems of second order arithmetic with restricted induction, I, II (abstracts), The Journal of Symbolic Logic, vol. 41 (1976), pp. 557–559.
[3] Harvey M., Friedman and Jeffry L., Hirst, Weak comparability of well orderings and reverse mathematics,Annals of Pure and Applied Logic, vol. 47 (1990), pp. 11–29.
[4] Jeffry L., Hirst, Reverse mathematics and ordinal exponentiation,Annals of Pure and Applied Logic, vol. 66 (1994), pp. 1–18.
[5] Jeffry L., Hirst, Ordinal inequalities, transfinite induction, and reverse mathematics,The Journal of Symbolic Logic, vol. 64 (1999), pp. 769–774.
[6] Jeffry L., Hirst, A survey of the reverse mathematics of ordinal arithmetic,Reverse mathematics 2001 (S., Simpson, editor), Lecture Notes in Logic, vol. 22, AK, Peters, 2005, this volume, pp. 222–234.Google Scholar
[7] James P., Jones, Hilbert, Levitz, and Warren D., Nichols, On series of ordinals and combinatorics,Mathematical Logic Quarterly, vol. 43 (1997), pp. 121–133.
[8] Wacław, Sierpiński, Cardinal and ordinal numbers, Polska Akademia Nauk, Monografie Matematyczne. Tom 34, Państwowe Wydawnictwo Naukowe, Warsaw, 1958.
[9] Stephen G., Simpson, Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin/Heidelberg, 1999.

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