Model theory without choice: Categoricity
Abstract
We prove Los conjecture = Morley theorem in ZF, with the same characterization (of first order countable theories categorical in alephalpha 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 alephalpha is either >=|alpha| for every alephα or it has a small upper bound (close to beth2).
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