Boney, WillCsima, Barbara F.Day, Nancy A.Harrison-Trainor, Matthew2023-07-242023-07-242023-03-15https://doi.org/10.1017/bsl.2023.1http://hdl.handle.net/10012/19630© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.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.enAttribution 4.0 Internationalextensions of first order logicinfinitarily definable classespseudo-elementary classesinfinitary logicArticle