Sh:E46

• Shelah, S. (2009). Categoricity of an abstract elementary class in two successive cardinals, revisited. In Classification Theory for Abstract Elementary Classes II.
  Ch. 6 of [Sh:i]
• 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 {\frak K} is categorical in \lambda,\lambda^+, LS({\frak K}) \le \lambda and has intermediate number of models in \lambda^{++}, then {\frak K} has a model in \lambda^{+++}.
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@inbook{Sh:E46,
 author = {Shelah, Saharon},
 title = {{Categoricity of an abstract  elementary class in two successive cardinals, revisited}},
 booktitle = {{Classification Theory for Abstract Elementary Classes II}},
 year = {2009},
 note = {Ch. 6 of [Sh:i]},
 refers_to_entry = {Ch. 6 of [Sh:i]}
}