Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-23T20:42:13.509Z Has data issue: false hasContentIssue false
  • English
  • Français

Order types of ordinals in models of set theory

Published online by Cambridge University Press:  12 March 2014

John E. Hutchinson
John E. Hutchinson*
Affiliation:
Australian National University, Canberra, A.C.T. 2600, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

An ordinal in a model of set theory is truly countable if its set of predecessors is countable in the real world. We classify the order types of the sets of truly countable ordinals. Models with indiscernibles and other related results are discussed.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 2 , June 1976 , pp. 489 - 502
Copyright
Copyright © Association for Symbolic Logic 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Conway, J. H., Ph.D. Thesis, Cambridge, England.Google Scholar
[2] Friedman, H., Countable models of set theories, Cambridge Summer School in Mathematical Logic, 1971, Lecture Notes in Mathematics, Springer-Verlag, Berlin, vol. 337 (1973), pp. 539–573.Google Scholar
[3] Hutchinson, J. E., Extending countable models of set theory, Notices of the American Mathematical Society, vol. 21 (1974), p. A–322, Abstract #74T-E31.Google Scholar
[4] Hutchinson, J. E., Elementary extensions of countable models of set theory, this Journal, vol. 41 (1976).Google Scholar
[5] Hutchinson, J. E., Model theory via set theory, Israel Journal of Mathematics (to appear).Google Scholar
[6] Keisler, H. J. and Morley, M., Elementary extensions of models of set theory, Israel Journal of Mathematics, vol. 6 (1968), pp. 49–65.CrossRefGoogle Scholar
[7] Morley, M., Partitions and models, Proceedings of the Summer School in Logic Leeds, 1967, Lecture Notes in Mathematics, Springer-Verlag, Berlin, vol. 70 (1968), pp. 109–158.CrossRefGoogle Scholar
[8] Silver, J. H., Some applications of model theory in set theory, Annals of Mathematics Logic, vol. 3 (1971), pp. 45–110.CrossRefGoogle Scholar
[9] Schmerl, J. H. and Shelah, S., On power-like models for hyperinaccessible cardinals, this Journal, vol. 37 (1972), pp. 531–537.Google Scholar