The primal framework II: smoothness

J. T. Baldwin; S. Shelah

doi:10.1016/0168-0072(91)90095-4

The primal framework II: smoothness

J. T. Baldwin^*
, S. Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1-34
Number of pages	34
Journal	Annals of Pure and Applied Logic
Volume	55
Issue number	1
DOIs	https://doi.org/10.1016/0168-0072(91)90095-4
State	Published - 28 Nov 1991

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The primal framework II: smoothness

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