TY - JOUR
T1 - The primal framework II
T2 - smoothness
AU - Baldwin, J. T.
AU - Shelah, S.
PY - 1991/11/28
Y1 - 1991/11/28
N2 - Let (K, ≤, cpr) be a class of models with a notion of 'strong' submodel and of canonically prime model (cpr) over an increasing chain. We show under appropriate set-theoretic hypotheses that if K is not smooth (there are incompatible models over some chains), then K has many models in certain cardinalities. On the other hand, if K is smooth, we show that in reasonable cardinalities K has a unique homogeneous-universal model. In this situation we introduce the notion of type and prove the equivalence of saturated with homogeneous-universal.
AB - Let (K, ≤, cpr) be a class of models with a notion of 'strong' submodel and of canonically prime model (cpr) over an increasing chain. We show under appropriate set-theoretic hypotheses that if K is not smooth (there are incompatible models over some chains), then K has many models in certain cardinalities. On the other hand, if K is smooth, we show that in reasonable cardinalities K has a unique homogeneous-universal model. In this situation we introduce the notion of type and prove the equivalence of saturated with homogeneous-universal.
UR - http://www.scopus.com/inward/record.url?scp=0038997290&partnerID=8YFLogxK
U2 - 10.1016/0168-0072(91)90095-4
DO - 10.1016/0168-0072(91)90095-4
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AN - SCOPUS:0038997290
SN - 0168-0072
VL - 55
SP - 1
EP - 34
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 1
ER -