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Elementary Properties of Cycle-free Partial Orders and their Automorphism Groups

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Abstract

A classification was given by Creed, Truss, and Warren of all the countable k-CS-transitive cycle-free partial orders for k≥3. Here the elementary theories of these structures and their automorphism groups are examined, and it is shown that in many cases we can distinguish the structures or their groups by means of their first- or second-order properties. The small index property is established for weakly 2-transitive trees, and for several classes of cycle-free partial orders.

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  1. Department of Pure Mathematics, University of Leeds, LS2 9JI, Leeds, United Kingdom

    J. K. Truss

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  1. J. K. Truss
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Truss, J.K. Elementary Properties of Cycle-free Partial Orders and their Automorphism Groups. Order 18, 359–379 (2001). https://doi.org/10.1023/A:1013987808448

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