Sh:E106

• Shelah, S. Lecture on: Categoricity of atomic classes in small cardinals in ZFC. Preprint.
  [Sh:F2195]
• Abstract:
  An atomic class K is the class of atomic first order models of a countable first order theory (assuming there are sucj models. Under the weak GCH it had been proved that if such class is categorical in every \aleph _n then is is categorical in every cardinal and is so called excellent, and results when we assume categoricity for \aleph _1, \dots, \aleph _n. The lecture is on a ZFC result in this direction for n=1. More specifically if K is categorical in \aleph _1 and has a model of cardinality > 2^{\aleph_0} then is is {\aleph_0}-stable, which implies having stable amalgamation, and is the first case of excellence

  This a work in preparation by Baldwin, J. T., Laskowski, M. C. and Shelah, S.

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@article{Sh:E106,
 author = {Shelah, Saharon},
 title = {{Lecture on: Categoricity of atomic classes in small cardinals in ZFC}},
 note = { [Sh:F2195]},
 refers_to_entry = { [Sh:F2195]}
}