Classes and theories of trees associated with a class of linear orders

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dc.contributor.author Goranko, Valentin
dc.contributor.author Kellerman, Ruaan
dc.date.accessioned 2012-10-11T06:12:16Z
dc.date.available 2012-10-11T06:12:16Z
dc.date.issued 2010-08
dc.identifier.citation Goranko, V. & Kellerman, R. 2011. Classes and theories of trees associated with a class of linear orders. Logic Journal of the IGPL, 19(1):217-232. [http://jigpal.oxfordjournals.org/] en_US
dc.identifier.issn 1367-0751
dc.identifier.uri http://hdl.handle.net/10210/7849
dc.description.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 analyzing first-order definable and undefinable paths in trees. en_US
dc.language.iso en en_US
dc.publisher Oxford University Press en_US
dc.rights © The Author 2010. Published by Oxford University Press. All rights reserved. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Logic Journal of the IGPL following peer review. The definitive publisher-authenticated version Goranko, V & Kellerman, R 2011, 'Classes and theories of trees associated with a class of linear orders', Logic Journal of the IGPL, vol. 19, no. 1, pp.217-232 is available online at: doi:10.1093/jigpal/jzq043. en_US
dc.subject Linear orders en_US
dc.subject First-order theories en_US
dc.subject Nondefinable paths en_US
dc.subject Trees (Graph theory) en_US
dc.title Classes and theories of trees associated with a class of linear orders en_US
dc.type Article en_US

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