# 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 -
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}, mrnumber = {2548468}, mrclass = {03C45 (03C75)}, doi = {10.2178/jsl/1245158091} }