Which Classes of Structures are Both Pseudo-Elementary and Definable by an Infinitary Sentence
Loading...
Date
2023-03-15
Authors
Boney, Will
Csima, Barbara F.
Day, Nancy A.
Harrison-Trainor, Matthew
Advisor
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