The spectrum of resplendency

Journal of Symbolic Logic 55 (2):626-636 (1990)
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Abstract

Let T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2 λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least $\min(2^\lambda,\beth_2)$ resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, 2 ω } there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ

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References found in this work

Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
On the Number of Strongly ℵ< Sub> Ε-Saturated Models of Power Λ.Saharon Shelah - 1987 - Annals of Pure and Applied Logic 36 (C):279-287.
Finite Diagrams Stable in Power.Saharon Shelah - 1970 - Annals of Mathematical Logic 2 (1):69.
On the Number of Strongly ℵϵ-Saturated Models of Power Λ.Saharon Shelah - 1987 - Annals of Pure and Applied Logic 36:279-287.

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