DISJOINT AMALGAMATION IN LOCALLY FINITE AEC

@article{Baldwin2017DISJOINTAI,
  title={DISJOINT AMALGAMATION IN LOCALLY FINITE AEC},
  author={John T. Baldwin and Martin Koerwien and Michael C. Laskowski},
  journal={The Journal of Symbolic Logic},
  year={2017},
  volume={82},
  pages={98 - 119}
}
Abstract We introduce the concept of a locally finite abstract elementary class and develop the theory of disjoint $\left( { \le \lambda ,k} \right)$ -amalgamation) for such classes. From this we find a family of complete ${L_{{\omega _1},\omega }}$ sentences ${\phi _r}$ that a) homogeneously characterizes ${\aleph _r}$ (improving results of Hjorth [11] and Laskowski–Shelah [13] and answering a question of [21]), while b) the ${\phi _r}$ provide the first examples of a class of models of a… 

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