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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 3.5.6): If λ i : i ≤ α < ℵ 1 is a strictly increasing sequence of characterizable cardinals (Definition 2.1) whose models satisfy JEP(< λ 0), there is an Lω 1… (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 characterizable by a Scott sentence and β < ω1, then ℵ α+β is characterizable by a Scott sentence. If 0 < γ < ω1, then the same is true for 2 ℵ α+γ. Also, ℵ ℵ… (More)

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