TY - JOUR
T1 - Transfering saturation, the finite cover property, and stability
AU - Baldwin, John T.
AU - Grossberg, Rami
AU - Shelah, Saharon
PY - 1999/6
Y1 - 1999/6
N2 - 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 >+, stability is equivalent to fo: all μ ≥ |T|, saturation is (μ, 2μ)-transferable.
AB - 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 >+, stability is equivalent to fo: all μ ≥ |T|, saturation is (μ, 2μ)-transferable.
UR - http://www.scopus.com/inward/record.url?scp=0033410016&partnerID=8YFLogxK
U2 - 10.2307/2586492
DO - 10.2307/2586492
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AN - SCOPUS:0033410016
SN - 0022-4812
VL - 64
SP - 678
EP - 684
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 2
ER -