In this paper we study abstract elementary classes with Löwenheim-Skolem number , where is cofinal with , which have finite character. We generalize results obtained by Kueker for . In particular, we show that is closed under -elementary equivalence and obtain sufficient conditions for to be -axiomatizable. In addition, we provide an example to illustrate that if is uncountable regular then is not closed under -elementary equivalence.
"Abstract Elementary Classes with Löwenheim-Skolem Number Cofinal with ω." Notre Dame J. Formal Logic 51 (3) 361 - 371, 2010. https://doi.org/10.1215/00294527-2010-022