Ordered asymptotic classes of finite structures

DOI10.1016/J.APAL.2019.102776arXiv1410.2615WikidataQ126402310 ScholiaQ126402310MaRDI QIDQ6255370

Publication date: 9 October 2014

Abstract: In this paper we introduce the concept of O-asymptotic classes of finite structures, melding ideas coming from 1-dimensional asymptotic classes and o-minimality. The results we present here include a cell-decomposition result for O-asymptotic classes and a classification of their infinite ultraproducts: Every infinite ultraproduct of structures in an O-asymptotic class is superrosy of U-thorn-rank 1, and NTP2 (in fact, inp-minimal).

Mathematics Subject Classification ID

Model theory of finite structures (03C13) Classification theory, stability, and related concepts in model theory (03C45) Ultraproducts and related constructions (03C20) Model theory of ordered structures; o-minimality (03C64)

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