We say that a countable model M completely characterizes an infinite cardinal κ , if the Scott sentence of M has a model in cardinality κ , but no models in cardinality κ. If a structure M completely… (More)

In partial answer to a question posed by Arnie Miller [5] and X. Caicedo [2] we obtain sufficient conditions for an Lω1,ω theory to have an independent axiomatization. As a consequence we obtain two… (More)

In [13] the authors show that if μ is a strongly compact cardinal, K is an Abstract Elementary Class (AEC) with LS(K) < μ, and K satisfies joint embedding (amalgamation) cofinally below μ, then K… (More)

Building on [4], [8] and [9] we study which cardinals are characterizable by a Scott sentence, in the sense that φM characterizes κ, if it has a model of size κ, but not of κ. We show that if אα is… (More)

We introduce the notion of a ‘pure’ Abstract Elementary Class to block trivial counterexamples. We study classes of models of bipartite graphs and show: Main Theorem (cf. Theorem 3.5.2 and Corollary… (More)