Archive for Mathematical Logic 30 (4):231-240 (1990)

We introduce a natural class of quantifiersTh containing all monadic type quantifiers, all quantifiers for linear orders, quantifiers for isomorphism, Ramsey type quantifiers, and plenty more, showing that no sublogic ofL ωω (Th) or countably compact regular sublogic ofL ∞ω (Th), properly extendingL ωω , satisfies the uniform reduction property for quotients. As a consequence, none of these logics satisfies eitherΔ-interpolation or Beth's definability theorem when closed under relativizations. We also show the failure of both properties for any sublogic ofL ∞ω (Th) in which Chang's quantifier or some cardinality quantifierQ α, with α≧1, is definable
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DOI 10.1007/BF01792985
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References found in this work BETA

Definability Hierarchies of General Quantifiers.Lauri Hella - 1989 - Annals of Pure and Applied Logic 43 (3):235.
Remarks in Abstract Model Theory.Saharon Shelah - 1985 - Annals of Pure and Applied Logic 29 (3):255-288.
Stationary Logic and its Friends. I.Alan H. Mekler & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):129-138.
Vector Spaces and Binary Quantifiers.Michał Krynicki, Alistair Lachlan & Jouko Väänänen - 1984 - Notre Dame Journal of Formal Logic 25 (1):72-78.
Stationary Logic and its Friends. II.Alan H. Mekler & Saharon Shelah - 1986 - Notre Dame Journal of Formal Logic 27 (1):39-50.

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