Authors: Tanović, Predrag 
Moconja, Slavko
Ilić, Dejan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: AROUND RUBIN’S “THEORIES OF LINEAR ORDER”
Journal: The Journal of Symbolic Logic
Volume: 85
Issue: 4
First page: 1403
Last page: 1426
Issue Date: 27-Oct-2020
Rank: M22
ISSN: 0022-4812
DOI: 10.1017/jsl.2020.68
Abstract: 
Let M= (M,<,...) be a linearly ordered first-order structure and T its complete theory. We investigate conditions for T that could guarantee that M is not much more complex than some colored orders (linear orders with added unary predicates). Motivated by Rubin’s work [5], we label three conditions expressing properties of types of T and/or automorphisms of models of T. We prove several results which indicate the “geometric” simplicity of definable sets in models of theories satisfying these conditions. For example, we prove that the strongest condition characterizes, up to definitional equivalence (inter-definability), theories of colored orders expanded by equivalence relations with convex classes
Publisher: Cambridge University Press

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