Which Classes of Structures are Both Pseudo-Elementary and Definable by an Infinitary Sentence
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When classes of structures are not first-order definable, we might still try to find a nice description. There are two common ways for doing this. One is to expand the language, leading to notions of pseudo-elementary classes, and the other is to allow infinite conjuncts and disjuncts. In this paper we examine the intersection. Namely, we address the question: Which classes of structures are both pseudo elementary and Lω1,ω-elementary? We find that these are exactly the classes that can be defined by an infinitary formula that has no infinitary disjunctions.
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Will Boney, Barbara F. Csima, Nancy A. Day, Matthew Harrison-Trainor (2023). Which Classes of Structures are Both Pseudo-Elementary and Definable by an Infinitary Sentence. UWSpace. http://hdl.handle.net/10012/19630
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