Sh:927

• Baldwin, J. T., Kolesnikov, A. S., & Shelah, S. (2009). The amalgamation spectrum. J. Symbolic Logic, 74(3), 914–928. DOI: 10.2178/jsl/1245158091 MR: 2548468
  See [Sh:927a]
• Abstract:
  For every natural number k^*, there is a class {\mathbf{K}}_* defined by a sentence in L_{\omega_1,\omega} that has no models of cardinality > \beth_{k^*+1}, but {\mathbf{K}}_* has the d isjoint amalgamation property on models of cardinality \leq \aleph_{{k^*}-3} and has models of cardinality \aleph_{{k^*}-1}. More strongly, For every countable ordinal \alpha^*, there is a class {\mathbf{K}}_* defined by a sentence in L_{\omega_1,\omega} that has no models of cardinality > \beth_{\alpha}, but {\mathbf{K}}_* has the disjoint amalgamation property on models of cardinality \leq \aleph_{\alpha}. Similar results hold for arbitrary \kappa and L_{\kappa^+,\omega}.
• published version (16p)

@article{Sh:927,
 author = {Baldwin, John T. and Kolesnikov, Alexei S. and Shelah, Saharon},
 title = {{The amalgamation spectrum}},
 journal = {J. Symbolic Logic},
 fjournal = {The Journal of Symbolic Logic},
 volume = {74},
 number = {3},
 year = {2009},
 pages = {914--928},
 issn = {0022-4812},
 mrnumber = {2548468},
 mrclass = {03C45 (03C75)},
 doi = {10.2178/jsl/1245158091},
 referred_from_entry = {See [Sh:927a]}
}