Classes and Theories of Trees Associated with a Class Of Linear Orders

Valentin Goranko, Ruaan Kellerman

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of the first-order theory of the generating class C, and indicate the problems obstructing such general results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees.
    Original languageEnglish
    JournalLogic Journal of the IGPL
    Volume19
    Issue number1
    Pages (from-to)217-232
    ISSN1367-0751
    DOIs
    Publication statusPublished - 2011

    Keywords

    • First-order theories
    • Trees
    • Definable and non-definable paths
    • Linear orders

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