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Model theory without choice: Categoricity
We 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_\alpha or it has a
small upper bound (close to beth_2)