## Journal of Symbolic Logic

### Transfering Saturation, The Finite Cover Property, and Stability

#### Abstract

$\underline{\text{Saturation is} (\mu, \kappa)-\text{transferable in} T}$ 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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745801

Mathematical Reviews number (MathSciNet)
MR1777778

Zentralblatt MATH identifier
0929.03041

JSTOR