2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164383We prove Los conjecture = Morley theorem in ZF, with the same characterization (of first order countable theories categorical in aleph_alpha for some (equivalently for every) ordinal alpha>0. Another central result here is, in this context: the number of models of a countable first order T of cardinality aleph_alpha is either >=|alpha| for every aleph_αor it has a small upper bound (close to beth_2).Logictext