# Sh:576

- Shelah, S. (2001).
*Categoricity of an abstract elementary class in two successive cardinals*. Israel J. Math.,**126**, 29–128. arXiv: math/9805146 DOI: 10.1007/BF02784150 MR: 1882033 -
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} }