Stationary sets and infinitary logic

Journal of Symbolic Logic 65 (3):1311-1320 (2000)

Authors
Jouko A Vaananen
University of Helsinki
Abstract
Let K 0 λ be the class of structures $\langle\lambda, , where $A \subseteq \lambda$ is disjoint from a club, and let K 1 λ be the class of structures $\langle\lambda, , where $A \subseteq \lambda$ contains a club. We prove that if $\lambda = \lambda^{ is regular, then no sentence of L λ+κ separates K 0 λ and K 1 λ . On the other hand, we prove that if $\lambda = \mu^+,\mu = \mu^{ , and a forcing axiom holds (and ℵ L 1 = ℵ 1 if μ = ℵ 0 ), then there is a sentence of L λλ which separates K 0 λ and K 1 λ
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DOI 10.2307/2586701
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References found in this work BETA

Internal Cohen Extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
Trees and Ehrenfeucht–Fraı̈ssé Games.Stevo Todorčević & Jouko Väänänen - 1999 - Annals of Pure and Applied Logic 100 (1-3):69-97.
Trees and Ehrenfeucht–Fraı̈ssé Games.Jouko Väänänen & Stevo Todorcevic - 1999 - Annals of Pure and Applied Logic 100 (1-3):69-97.

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