Notre Dame Journal of Formal Logic

Upward Stability Transfer for Tame Abstract Elementary Classes

John Baldwin, David Kueker, and Monica VanDieren

Abstract

Grossberg and VanDieren have started a program to develop a stability theory for tame classes. We name some variants of tameness and prove the following. Let K be an AEC with Löwenheim-Skolem number ≤κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then K is Galois-stable in κ⁺ⁿ for all n<ω. With one further hypothesis we get a very strong conclusion in the countable case. Let K be an AEC satisfying the amalgamation property and with Löwenheim-Skolem number ℵ₀ that is ω-local and ℵ₀-tame. If K is ℵ₀-Galois-stable then K is Galois-stable in all cardinalities.

Article information

Source
Notre Dame J. Formal Logic, Volume 47, Number 2 (2006), 291-298.

Dates
First available in Project Euclid: 25 July 2006

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1153858652

Digital Object Identifier
doi:10.1305/ndjfl/1153858652

Mathematical Reviews number (MathSciNet)
MR2240625

Zentralblatt MATH identifier
1113.03028

Subjects
Primary: 03C45: Classification theory, stability and related concepts [See also 03C48] 03C52: Properties of classes of models 03C75: Other infinitary logic
Secondary: 03C05: Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05] 03C55: Set-theoretic model theory 03C95: Abstract model theory

Keywords
stability theory tameness abstract elementary class

Citation

Baldwin, John; Kueker, David; VanDieren, Monica. Upward Stability Transfer for Tame Abstract Elementary Classes. Notre Dame J. Formal Logic 47 (2006), no. 2, 291--298. doi:10.1305/ndjfl/1153858652. https://projecteuclid.org/euclid.ndjfl/1153858652


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References

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