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NIP omega-categorical structures: the rank 1 case

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arxiv 1807.07102 v5 pith:BGVASE4N submitted 2018-07-18 math.LO math.CO

classification math.LOmath.CO
keywords structuresmanyfinitelylinearnumberomega-categoricalordersprimitive
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We classify primitive, rank 1, omega-categorical structures having polynomially many types over finite sets. For a fixed number of 4-types, we show that there are only finitely many such structures and that all are built out of finitely many linear orders interacting in a restricted number of ways. As an example of application, we deduce the classification of primitive structures homogeneous in a language consisting of n linear orders as well as all reducts of such structures.

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  1. Structures with not too fast unlabelled growth

    math.LO 2025-07 conditional novelty 7.0 of 10

    A complete classification of ω-categorical structures with unlabelled growth below 2^n/p(n), confirming Thomas' conjecture and giving optimal growth gaps for this class.

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