A semilinear space S is ultrahomogeneous if each isomorphism between the semilinear structures induced on two nite subsets can be extended to an automorphism of S. We give a complete classication of all nite ultrahomogeneous semilinear spaces. Our theorem extends a result of Gardiner on graphs and a result of Devillers and Doyen on linear spaces. 2000 Mathematics Subject Classication: 05B25, 51E14, 20B25. 1
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