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Model theory without choice? Categoricity

  • Saharon Shelah (a1) (a2)


We prove Los conjecture = Morley theorem in ZF. with the same characterization, i.e., of first order countable theories categorical in ℵα for some (eqiuvalently 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 ⊐2).



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  • ISSN: 0022-4812
  • EISSN: 1943-5886
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