Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T15:27:59.619Z Has data issue: false hasContentIssue false
  • English
  • Français

Transfering saturation, the finite cover property, and stability

Published online by Cambridge University Press:  12 March 2014

John T. Baldwin ,
Rami Grossberg  and
Saharon Shelah
John T. Baldwin
Affiliation:
Department of Mathematics, University of Illinois at Chicago, Chicago, IL 60680., USA E-mail: [email protected]
Rami Grossberg
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh. Pa 15213, USA E-mail: [email protected]
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91094, Israel Department of Mathematics, Rutgers University, New Brunswick. NJ 08902, USA E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Saturation is (μ, κ)-transferable in T if and only if there is an expansion T1 of T with |T1| = |T| such that if M is a μ-saturated model of T1 and |M| ≥ κ then the reduct M|L(T) is κ-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is (ℵ0, λ)-transferable or (κ(T), λ)-transferable for all λ. Further if for some μ ≥ |T|,2μ > μ+, stability is equivalent to for all μ ≥ |T|, saturation is (μ, 2μ)-transferable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 678 - 684
Copyright
Copyright © Association for Symbolic Logic 1999

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

[Ca] Casanovas, Enrique, Compactly expandable models and stability, this Journal, vol. 60 (1995), pp. 673–683.Google Scholar
[CK] Chang, C.C. and Keisler, H. Jerome, Model Theory, North-Holland Publ. Co., 1990.Google Scholar
[Ke] Keisler, H. Jerome, Ultraproducts which are not saturated, this Journal, vol. 32 (1967), pp. 23–46.Google Scholar
[Ku] Kunen, Kenneth, Ultrafilters and independent sets, Transactions of the American Mathematical Society, vol. 172 (1972), pp. 199–206.Google Scholar
[Sh:10] Shelah, Saharon, Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory, Annals of Mathematical Logic, vol. 3 (1971), pp. 271–362, —MR: 47:6475, (02H05).Google Scholar
[Sh:c] Shelah, Saharon, Classification Theory and the Number of Nonisomorphic Models, rev. ed., North-Holland, Amsterdam, 1990.Google Scholar