Which Classes of Structures Are Both Pseudo-elementary and Definable by an Infinitary Sentence?

Will Boney; Barbara F. Csima; Nancy A. Day; Matthew Harrison-Trainor

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arXiv · 1808.01588

Which Classes of Structures Are Both Pseudo-elementary and Definable by an Infinitary Sentence?

Will Boney·Barbara F. Csima·Nancy A. Day·Matthew Harrison-Trainor

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Abstract

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 $\mathcal{L}_{\omega_1 \omega}$-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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BibTeX RIS

Will Boney, Barbara F. Csima, Nancy A. Day, Matthew Harrison-Trainor. 2018-08-05. Which Classes of Structures Are Both Pseudo-elementary and Definable by an Infinitary Sentence?. https://arxiv.org/abs/1808.01588

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