Re.v,cota Coiomb~aYla de. Mate.matic.a.-6 Vol. XX (1986), p6.g-6. 1- 2 6 EL RETICULa DE LAS LOGICAS DE PRIMER ORDEN CON CUANTIFICADORES CARDINALES* par Luis Jaime CORREDOR ABSTRACT. Associate to every class S of car- dinals a quantifier QS so that QSx~{x) holds just in case the number of individuals satisfying ~(x) is a cardinal belonging to S. This includes the well know cardinal quantifiers Qa' We give a sim- ple combinatorial condition on the classes Sand S' necessary and sufficient to have A similar result is shown for logics generated by families of such quantifiers. Some applications follow; for example, it is shown that if nw de- notes the set of multiples of the natural number n, then Lww{QDw) ~ Lww{QIDW) if and only if n di- vides m. Also, we construct infinite descending chains of logics. * Este trabajo se basa en la tesis de Magister del autor, Universidad de los Andes, Bogota, 1983, realizada bajo la direccion del Profesor X. Caicedo.