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

Bulletin of Symbolic Logic 29 (1):1-18 (2023)
  Copy   BIBTEX

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,296

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Karp complexity and classes with the independence property.M. C. Laskowski & S. Shelah - 2003 - Annals of Pure and Applied Logic 120 (1-3):263-283.
From noncommutative diagrams to anti-elementary classes.Friedrich Wehrung - 2020 - Journal of Mathematical Logic 21 (2):2150011.
On Sahlqvist Formulas in Relevant Logic.Guillermo Badia - 2018 - Journal of Philosophical Logic 47 (4):673-691.
Computable axiomatizability of elementary classes.Peter Sinclair - 2016 - Mathematical Logic Quarterly 62 (1-2):46-51.
Abstract elementary classes and infinitary logics.David W. Kueker - 2008 - Annals of Pure and Applied Logic 156 (2):274-286.
The categoricity spectrum of pseudo-elementary classes.Michael Chris Laskowski - 1992 - Notre Dame Journal of Formal Logic 33 (3):332-347.

Analytics

Added to PP
2023-03-15

Downloads
6 (#1,485,580)

6 months
4 (#862,833)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references