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Transfering saturation, the finite cover property, and stability

Published online by Cambridge University Press:  12 March 2014

John T. Baldwin
Affiliation:
Department of Mathematics, University of Illinois at Chicago, Chicago, IL 60680., USA E-mail: jbaldwin@uic.edu
Rami Grossberg
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh. Pa 15213, USA E-mail: rami@cmu.edu
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: shelah@sunrise.huji.ac.il

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
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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