Sh:840

• Shelah, S. (2009). Model theory without choice? Categoricity. J. Symbolic Logic, 74(2), 361–401.
• Abstract:
The main result is Łos conjecture: characterizing in ZF of countable first order T categoricity in some uncountable \aleph_\alpha (or every one). If there are \aleph_1 real this is Morley’s theorem, the ZFC one. Otherwise, we get a different theorem. The characterization (and the proof) are different.
• Version 2008-07-03_10 (61p) published version (42p)
Bib entry
@article{Sh:840,
author = {Shelah, Saharon},
title = {{Model theory without choice? Categoricity}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {74},
number = {2},
year = {2009},
pages = {361--401},
issn = {0022-4812},
mrnumber = {2518563},
mrclass = {03C45 (03E25)},
doi = {10.2178/jsl/1243948319},
note = {\href{https://arxiv.org/abs/math/0504196}{arXiv: math/0504196}},
arxiv_number = {math/0504196}
}