# Sh:576

• Shelah, S. (2001). Categoricity of an abstract elementary class in two successive cardinals. Israel J. Math., 126, 29–128.
• Abstract:
We investigate categoricity of abstract elementary classes without any remnants of compactness (like non-definability of well ordering, existence of E.M. models or existence of large cardinals). We prove (assuming a weak version of GCH around \lambda) that if \mathfrak{K} is categorical in \lambda,\lambda^+, LS(\mathfrak{K}) \le\lambda and 1\le I(\lambda^{++},\mathfrak{K})< 2^{\lambda^{++}} then \mathfrak{K} has a model in \lambda^{+++}.
• published version (100p)
Bib entry
@article{Sh:576,
author = {Shelah, Saharon},
title = {{Categoricity of an abstract elementary class in two successive cardinals}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {126},
year = {2001},
pages = {29--128},
issn = {0021-2172},
mrnumber = {1882033},
mrclass = {03C95 (03C45)},
doi = {10.1007/BF02784150},
note = {\href{https://arxiv.org/abs/math/9805146}{arXiv: math/9805146}},
arxiv_number = {math/9805146}
}