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THE STABILITY SPECTRUM FOR CLASSES OF ATOMIC MODELS

    https://doi.org/10.1142/S0219061312500018Cited by:3 (Source: Crossref)

    We prove two results on the stability spectrum for Lω1. Here denotes an appropriate notion (at or mod) of Stone space of m-types over M. (1) Theorem for unstable case: Suppose that for some positive integer m and for every α < δ(T), there is an M ∈ K with . Then for every λ ≥ |T|, there is an M with . (2) Theorem for strictly stable case: Suppose that for every α < δ (T), there is MαK such that λα = |Mα| ≥ ℶα and . Then for any μ with μ0 > μ, K is not i-stable in μ. These results provide a new kind of sufficient condition for the unstable case and shed some light on the spectrum of strictly stable theories in this context. The methods avoid the use of compactness in the theory under study. In this paper, we expound the construction of tree indiscernibles for sentences of Lω1. Further we provide some context for a number of variants on the Ehrenfeucht–Mostowski construction.

    AMSC: 03C45, 03C75

    References