caa a22 4500 465743706 CHVBK 20180323111814.0 cr unu---uuuuu 170327e19900701xx s 000 0 eng 10.1007/BF01792985 doi (NATIONALLICENCE)springer-10.1007/BF01792985 Caicedo Xavier Departamento de Matemáticas, Universidad Nacional de Colombia, Apartado aéreo 2509, Bogota, Colombia aut Definability properties and the congruence closure [Elektronische Daten] [Xavier Caicedo] 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. Springer-Verlag, 1990 Archive for Mathematical Logic Springer-Verlag 30/4(1990-07-01), 231-240 0933-5846 30:4<231 1990 30 153 https://doi.org/10.1007/BF01792985 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01792985 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Caicedo Xavier Departamento de Matemáticas, Universidad Nacional de Colombia, Apartado aéreo 2509, Bogota, Colombia aut NATIONALLICENCE 773 0- Archive for Mathematical Logic Springer-Verlag 30/4(1990-07-01), 231-240 0933-5846 30:4<231 1990 30 153 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer