# Sh:927

• Baldwin, J. T., Kolesnikov, A. S., & Shelah, S. (2009). The amalgamation spectrum. J. Symbolic Logic, 74(3), 914–928.
• 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)
Bib entry
@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},
doi = {10.2178/jsl/1245158091},
mrclass = {03C45 (03C75)},
mrnumber = {2548468},
mrreviewer = {Alfred Dolich},
doi = {10.2178/jsl/1245158091}
}