Journal of Symbolic Logic

Transfering Saturation, The Finite Cover Property, and Stability

John T. Baldwin, Rami Grossberg, and Saharon Shelah

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$\underline{\text{Saturation is} (\mu, \kappa)-\text{transferable in} T}$ if and only if there is an expansion T$_1$ of T with $\mid T_1 \mid$ = $\mid T \mid$ such that if M is a $\mu$-saturated model of T$_1$ and $\mid M \mid \geq \kappa$ then the reduct M $\mid L(T)$ is $\kappa$-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is ($\aleph_0, \lambda$)- transferable or ($\kappa (T), \lambda$)-transferable for all $\lambda$. Further if for some $\mu \geq \mid T \mid, 2^\mu > \mu^+$, stability is equivalent to for all $\mu \geq \mid T \mid$, saturation is ($\mu, 2^\mu$)- transferable.

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J. Symbolic Logic, Volume 64, Issue 2 (1999), 678-684.

First available in Project Euclid: 6 July 2007

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Baldwin, John T.; Grossberg, Rami; Shelah, Saharon. Transfering Saturation, The Finite Cover Property, and Stability. J. Symbolic Logic 64 (1999), no. 2, 678--684.

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