Sh:300f

• Shelah, S. (2009). Universal Classes: The heart of the matter. In Classification Theory for Abstract Elementary Classes II.
  Ch. V (F) of [Sh:i]
• Abstract:
  We prove a strong parallel of Erdős-Rado theorem with independence. This is used to get non-structure results from the order properties for the parallel of \Sigma_1-formulas. If this order property fails, we get a successor \mathfrak{s}^+ of the framework \mathfrak{s}, with a stronger notion of sub-models. The successor has most of the demands for being in our main framework, AxFr_1, but Ax(A4) [the existence of unions] is a dividing line, so again we deal with non-structure consequences of its failure.
• No downloadable versions available.

@inbook{Sh:300f,
 author = {Shelah, Saharon},
 title = {{Universal Classes: The heart of the matter}},
 booktitle = {{Classification Theory for Abstract Elementary Classes II}},
 year = {2009},
 note = {Ch. V (F) of [Sh:i]},
 refers_to_entry = {Ch. V (F) of [Sh:i]}
}