We prove łos conjecture=Morley theorem in ZF, with the same characterization, i.e., of first order countable theories categorical in ℵα for some (equivalently for every ordinal) α > 0. Another central result here in this context is: the number of models of a countable first order T of cardinality ℵα is either ≥ |α| for every α or it has a small upper bound (independent of α close to ℶ2).
"Model theory without choice? Categoricity." J. Symbolic Logic 74 (2) 361 - 401, June 2009. https://doi.org/10.2178/jsl/1243948319