Model theory without choice: Categoricity
Logic
2008-07-08 v3
Abstract
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).
Cite
@article{arxiv.math/0504196,
title = {Model theory without choice: Categoricity},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/0504196},
year = {2008}
}