Skip to main content
Journal of Symbolic LogicVolume 85, Issue 4, December 2020, Pages 1403-1426

AROUND RUBIN'S THEORIES of LINEAR ORDER(Article)(Open Access)

  • Tanovic, P.,
  • Moconja, S.,
  • Ilic¨, D.
  Save all to author list
  • aMathematical Institute Sanu, KNEZ MIHAILOVA 36, BELGRADE, 11000, Serbia
  • bUniversity of Belgrade, Faculty of Mathematics, STUDENTSKI TRG 16, BELGRADE, 11000, Serbia
  • cInstytut Matematyczny, Uniwersytet WROClAWSKI, PL. GRUNWALDZKI 2/4, WROCLAW, 50-384, Poland
  • dUniversity of Belgrade, Faculty of Transport and Traffic Engineering, VOJVODE STEPE 305, BELGRADE, 11000, Serbia

Abstract

Let <![CDATA[\mathcal M=(M, be a linearly ordered first-order structure and T its complete theory. We investigate conditions for T that could guarantee that 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. Copyright © 2021 by the Association for Symbolic Logic. All rights reserved.

Author keywords

2020 Mathematics Subject Classification 03C64 06A05

Funding details

Funding sponsor Funding number Acronym
Univerzitet u Beogradu
Ministarstvo Prosvete, Nauke i Tehnološkog RazvojaMPNTR
Narodowe Centrum Nauki2016/22/E/ST1/00450NCN

  • 1

    Proof of Theorem 1. It suffices to show that a saturated linearly ordered structure is definitionally equivalent with its ccel-reduct if and only if it satisfies (SLB). The right-to-left direction is a consequence of Theorem 2: (SLB) implies that every formula is equivalent with a Boolean combination of u-convex formulae which are expressible in the language of the ccel-reduct, too. The other direction is an immediate consequence of Lemma 2.6. \u22A3 Acknowledgments. The first author was supported by the Ministry of Education, Science and Technological Development of Serbia through Mathematical Institute SANU. The second author was supported by the Narodowe Centrum Nauki grant no. 2016/22/E/ST1/00450, and by the Ministry of Education, Science and Technological Development of Serbia through University of Belgrade, Faculty of Mathematics. The third author was supported by the Ministry of Education, Science and Technological Development of Serbia through University of Belgrade, Faculty of Transport and Traffic Engineering.

  • ISSN: 00224812
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1017/jsl.2020.68
  • Document Type: Article
  • Publisher: Cambridge University Press


© Copyright 2021 Elsevier B.V., All rights reserved.

Cited by 2 documents

Dauletiyarova, A.B. , Verbovskiy, V.V.
ON THE NUMBER OF COUNTABLE MODELS OF CONSTANT AND UNARY PREDICATES EXPANSIONS OF THE DENSE MEET-TREE THEORY
(2024) Siberian Electronic Mathematical Reports
Moconja, S. , Tanović, P.
Does weak quasi-o-minimality behave better than weak o-minimality?
(2022) Archive for Mathematical Logic
View details of all 2 citations
Inform me when this document is cited in Scopus:
Set citation alert Set citation feed
{"topic":{"name":"Simple Theory; Minimality; Number","id":10389,"uri":"Topic/10389","prominencePercentile":62.182346,"prominencePercentileString":"62.182","overallScholarlyOutput":0},"dig":"6d1305c4be4354b1ded52b8f2f9a5270f66e97270d7687bf5f15317b12463169"}

SciVal Topic Prominence

Topic:
Prominence percentile: