Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T23:02:30.848Z Has data issue: false hasContentIssue false
  • English
  • Français

On the existence of atomic models

Published online by Cambridge University Press:  12 March 2014

M. C. Laskowski  and
S. Shelah
M. C. Laskowski
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, E-mail: [email protected]
S. Shelah
Affiliation:
Department of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Get access Rights & Permissions [Opens in a new window]

Abstract

We give an example of a countable theory T such that for every cardinal λ ≥ ℵ2 there is a fully indiscernible set A of power λ such that the principal types are dense over A, yet there is no atomic model of T over A. In particular, T(A) is a theory of size λ where the principal types are dense, yet T(A) has no atomic model.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 4 , December 1993 , pp. 1189 - 1194
Copyright
Copyright © Association for Symbolic Logic 1993

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]Erdös, P., Hajnal, A., Mate, A., and Rado, P., Combinatorial set theory, North-Holland, Amsterdam, 1984.Google Scholar
[2]Knight, J., Prime and atomic models, this Journal, vol. 43 (1978), pp. 385–393.Google Scholar
[3]Kueker, D. W., Uniform theorems in infinitary logic, Logic Colloquium '77 (Macintyre, A., Pacholski, L., and Paris, J., editors), North-Holland, Amsterdam, 1978.Google Scholar
[4]Kueker, D. W. and Laskowski, M. C., On generic structures, Notre Dame Journal of Formal Logic, vol. 33 (1992), pp. 175–183.CrossRefGoogle Scholar
[5]Shelah, S., Classification theory, North-Holland, Amsterdam, 1978.Google Scholar