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Which Classes of Structures are Both Pseudo-Elementary and Definable by an Infinitary Sentence

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Date

2023-03-15

Authors

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

Journal Title

Journal ISSN

Volume Title

Publisher

Cambridge University Press

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 Lω1,ω-elementary? We find that these are exactly the classes that can be defined by an infinitary formula that has no infinitary disjunctions.

Description

© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.

Keywords

extensions of first order logic, infinitarily definable classes, pseudo-elementary classes, infinitary logic

LC Keywords

Citation

URI

https://doi.org/10.1017/bsl.2023.1
 http://hdl.handle.net/10012/19630

Collections

Waterloo Research