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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]
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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

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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