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Stationary sets and infinitary logic

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem, Israel
Jouko Väänänen
Affiliation:
Department of Mathematics, University of Helsinki, Helsinki, Finland

Abstract

Let be the class of structures 〈λ, <, A〉, where Aλ is disjoint from a club, and let be the class of structures 〈λ, <, A), where Aλ contains a club. We prove that if λ = λ<κ is regular, then no sentence of Lλ + κ separates and On the other hand, we prove that if λ = μ+ , μ = μ<μ, and a forcing axiom holds (and if μ = ℵ0), then there is a sentence of Lλλ which separates and .

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2000

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References

[1]Hyttinen, T., Model theory for infinite quantifier languages, Fundamenta Mathematicae, vol. 134 (1990), pp. 125–142.CrossRefGoogle Scholar
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