Browse > Article
http://dx.doi.org/10.14403/jcms.2011.24.4.5

ON ORDINALS  

Chung, Se Hwa (Department of Mathematics and Information Kyungwon University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.24, no.4, 2011 , pp. 675-686 More about this Journal
Abstract
The aim of this paper is two fold: One of them is to introduce a formal definition of ordinals which is equivalent to Neumann's definition without assuming the axiom of regularity. The other is to introduce the weak transfinite set and show that the weak transfinite set is a transfinite limit ordinal.
Keywords
ordinal; weak transfinite set; usual limit ordinal; transfinite limit ordinal;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. G. F. Belinfante, Robinson's (1937) definition of ordinal, 2008.
2 G. Cantor, Beitrage zur Begrundung der transfiniten Mengenlehre. II (tr.: Contributions to the Founding of the Theory of Transfinite s II), Mathematische Annalen 49, 207-246 English translation, 1897.   DOI   ScienceOn
3 J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1970.
4 A. G. Hamilton, Numbers, Sets and axioms, Cambridge University Press, New York, 1982.
5 K. Hrbacek and T. J. Jech, Introduction to Set Theory, Marcel Dekker, 2nd edition, 1984.
6 T. J. Jeck, Set Theory, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003.
7 J. L. Kelley, General Topology, Springer-Verlag, New York, 1955.
8 J. Maltiz, Introduction to Mathematical Logic, Springer-Verlag, New York Inc., 1979.
9 J. von Neumann, "An Axiomatization of Set Theory." English translation in Jean van Heijenoort, ed., 1967. From Frege to Godel: A Source Book in Math- ematical Logic, 1879-1931. Harvard University Press. 393 - 413, 1925.
10 J. R. Shoenfild, Axioms of Set Theory, Handbook of Mathematical Logic, Edited by Jon Barwise, Elsevier Science Publishers, 1977.
11 T. Skolem, Abstract Set Theory, University of Notre Dame, 1962.