Abstract
This paper concerns the classification of finite coloured linear orders up to n-equivalence. Ehrenfeucht–Fraïssé games are used to define what this means, and also to help analyze such structures. We give an explicit bound for the least number g(m,n) such that any finite m-coloured linear order is n-equivalent to some ordering of size ≤ g(m,n), from which it follows that g is computable. We give exact values for g(m,1) and g(m,2). The method of characters is developed and used.
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This paper is based on part of the first author’s Ph.D. thesis at the University of Leeds [2], which was supported by a Commonwealth Scholarship.
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Mwesigye, F., Truss, J.K. Classification of Finite Coloured Linear Orderings. Order 28, 387–397 (2011). https://doi.org/10.1007/s11083-010-9178-9
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DOI: https://doi.org/10.1007/s11083-010-9178-9