We sort out to a large extent when a (first order complete theory) T has a superlimit model in a cardinal λ. Also we deal with related notions of being limit.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-4, author = {Saharon Shelah}, title = {When a first order T has limit models}, journal = {Colloquium Mathematicae}, volume = {126}, year = {2012}, pages = {187-204}, zbl = {1260.03067}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-4} }
Saharon Shelah. When a first order T has limit models. Colloquium Mathematicae, Tome 126 (2012) pp. 187-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-2-4/