Une axiomatisation au premier ordre des arrangements de pseudodroites euclidiennes
Annales de l'Institut Fourier, Volume 49 (1999) no. 3, pp. 883-903.

We define a logical structure making it possible to represent arrangements of pseudolines in the Euclidean plane up to homeomorphism. We give a first-order axiomatisation of realizability of such structures by arrangements.

Nous définissons une structure logique permettant de représenter les classes d’homéomorphismes des arrangements de pseudodroites du plan euclidien. Nous donnons une axiomatisation finie du premier ordre de la réalisabilité des arrangements de pseudodroites.

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     title = {Une axiomatisation au premier ordre des arrangements de pseudodroites euclidiennes},
     journal = {Annales de l'Institut Fourier},
     pages = {883--903},
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Courcelle, Bruno; Olive, Frédéric. Une axiomatisation au premier ordre des arrangements de pseudodroites euclidiennes. Annales de l'Institut Fourier, Volume 49 (1999) no. 3, pp. 883-903. doi : 10.5802/aif.1697. https://aif.centre-mersenne.org/articles/10.5802/aif.1697/

[1] S.A. Adeleke and P.M. Neumann, Relations related to betweenness: their structure and automorphisms, Memoirs of the Amer. Math. Soc., 623 (1998). | MR | Zbl

[2] A. Björner, M. Las Vergnas, B. Sturmfels, N. White, and G. Ziegler, Oriented matroids, Encyclopedia of mathematics and its applications, Vol. 46, Cambridge University Press, 1993. | Zbl

[3] J.E. Goodman, Proof of a conjecture of Burr, Grunbaum and Sloane, Discrete Mathematics, 32 (1980), 27-35. | MR | Zbl

[4] Goodman, Pseudoline arrangements, In J.E. Goodman and J. O'Rourke, editors, Hanbook of Discrete and Computational Geometry, pages 83-109. CRC Press LLC, 1997. | MR | Zbl

[5] J.E. Goodman and R. Pollack, Semispaces of configurations, cell complexes of arrangements, Journal of Combinatorial Theory, Series A, 37 (1984), 257-293. | MR | Zbl

[6] J.E. Goodman, R. Pollack, R. Wenger, and T. Zamfirescu, Arrangements and topological planes, Amer. Math. Monthly, 101 (1994), 866-878. | MR | Zbl

[7] B. Grunbaum, Arrangements and spreads. In CBMS Regional Conference, volume 10 of Series in Math. Amer. Math. Soc., Providence, R.I., 1972. | MR | Zbl

[8] L. Ségoufin and V. Vianu, Spacial databases via topological invariants. Proc. ACM Symp. on Principles of Databases Systems, 1998 (version finale à paraître au J. Comput. Syst. Sciences).

[9] P.W. Shor, Stretchability of pseudolines is NP-hard. In Applied geometry and discrete mathematics, The Victor Klee Festschrift, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 4, 1991, 531-554. | MR | Zbl

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