. L O ] 9 J ul 1 99 8 TRANSFERING SATURATION , THE FINITE COVER PROPERTY , AND STABILITY ∗
نویسندگان
چکیده
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 |, 2 > μ+, stability is equivalent to for all μ ≥ |T |, saturation is (μ, 2)transferable.
منابع مشابه
Transfering Saturation, The Finite Cover Property, and Stability
Saturation is (μ, κ)-transferable in T if and only if there is an expansion T1 of T with |T1| ≤ |T | + א0 such that if M is a μ-saturated model of T1 and |M | ≥ κ then M |L(T ) is κ-saturated. Theorem A. The following are equivalent for a complete theory T . (1) T does not have the finite cover property. (2) ∀λ ≥ |T |+, saturation is (|T |+, λ)-transferable in T . (3) ∃λ > 2|T | such that satur...
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