Complexities of Relational Structures
-
David Hartman
,
Jan Hubička
Abstract
The relational complexity, introduced by G. Cherlin, G. Martin, and D. Saracino, is a measure of ultrahomogeneity of a relational structure. It provides an information on minimal arity of additional invariant relations needed to turn given structure into an ultrahomogeneous one. The original motivation was group theory. This work focuses more on structures and provides an alternative approach. Our study is motivated by related concept of lift complexity studied by Hubička and Nešetřil.
References
[1] CAMERON, P. J.: The age of a relational structure. In: Directions in Infinite Graph Theory and Combinatorics (R. Diestel, ed.). Topic in Discrete Math. 3, North-Holland, Amsterdam, 1992, pp. 49-67.Suche in Google Scholar
[2] CAMERON, P. J.-NEŠETŘIL, J.: Homomorphism-homogeneous relational structures, Combin. Probab. Comput. 15 (2006), 91-103.10.1017/S0963548305007091Suche in Google Scholar
[3] CHERLIN, G.: The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments, Mem. Amer. Math. Soc. 612 (1998), 1-161.Suche in Google Scholar
[4] CHERLIN, G.: Sporadic homogeneous structures. In: The Gelfand Mathematical Seminars (1994-1999), Birkhäuser Boston, 2000, 15-48.10.1007/978-1-4612-1340-6_2Suche in Google Scholar
[5] CHERLIN, G.: Two problems on homogeneous structures, revisited. In: Model Theoretic Methods in Finite Combinatorics (M. Grohe, J. A. Makowsky, eds.). Contemp. Math. 558, Amer. Math. Soc., Providence, RI, 2011, pp. 319-415.10.1090/conm/558/11055Suche in Google Scholar
[6] CHERLIN, G.-MARTIN, G.-SARACINO, D.: Arities of permutation groups: Wreath products and k-sets, J. Combin. Theory Ser. A 74 (1996), 249-286.10.1006/jcta.1996.0050Suche in Google Scholar
[7] CHERLIN, G. L.-SHELAH, S.-SHI, N.: Universal graphs with forbidden subgraphs and algebraic closure, Adv. in Appl. Math. 22 (1999), 454-491.10.1006/aama.1998.0641Suche in Google Scholar
[8] COVINGTON, J.: Homogenizable relational structures, Illinois J. Math. 34 (1990), 731-743.10.1215/ijm/1255988065Suche in Google Scholar
[9] FRÄISSÉ , R.: Sur certains relations qui généralisent l’ordre des nombres rationnels, C. R. Acad. Sci. Paris 237 (1953), 540-542.Suche in Google Scholar
[10] GARDINER, A.: Homogeneous graphs, J. Combin. Theory Ser. B 20 (1976), 94-102.10.1016/0095-8956(76)90072-1Suche in Google Scholar
[11] HODGES, W.: Model Theory, Cambridge University Press, Cambridge, 1993.Suche in Google Scholar
[12] HUBIČKA, J.-NEŠETŘIL, J.: Universal structures with forbidden homomorphisms. In: Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics (A. Hirvonen, J. Kontinen, R. Kossak, A. Villaveces, eds.). Ontos Math. Logic Ser., De Gruyter, Berlin, 2015, pp. 241-264.Suche in Google Scholar
[13] HUBIČKA, J.-NEŠETŘIL, J.: Homomorphism and embedding universal structures for restricted classes, J. Mult.-Valued Logic Soft Comput. (To appear).Suche in Google Scholar
[14] JENKINSON, T.-SEIDEL, D.-TRUSS, J. K.: Countable homogeneous multipartite graphs, European J. Combin. 33 (2012), 82-109.10.1016/j.ejc.2011.04.004Suche in Google Scholar
[15] KECHRIS, A. S.-PESTOV, V. G.-TODORČEVIČ, S.: Fräıssé limits, Ramsey theory, and topological dynamics of automorphism groups, Geom. Funct. Anal. 15 (2005), 106-189.10.1007/s00039-005-0503-1Suche in Google Scholar
[16] KNIGHT, J.-LACHLAN, A. Shrinking, stretching, and codes for homogeneous structures. In: Classification Theory (J. Baldwin, ed.). Lecture Notes in Math. 1292, Sringer, New York, 1985.Suche in Google Scholar
[17] LACHLAN, A. H.-WOODROW, A. H.: Countable ultra-homogeneous graphs, Trans. Amer. Math. Soc. 262 (1992), 51-94.10.1090/S0002-9947-1980-0583847-2Suche in Google Scholar
[18] NEŠETŘIL, J.-TARDIF, C.: Duality theorems for finite structures (Characterising gaps and good characterisations), J. Combin. Theory Ser. B 80 (2000), 80-97.10.1006/jctb.2000.1970Suche in Google Scholar
[19] MATOUŠEK, J-NEŠETŘIL, J.: Invitation to Discrete Mathematics, Oxford University Press, Oxford, 1998. 20] NEŠETŘIL, J.: For graphs there are only four types of hereditary Ramsey classes, J.Combin. Theory Ser. B 46 (1989), 127-132.10.1016/0095-8956(89)90038-5Suche in Google Scholar
[21] NEŠETŘIL, J.: Ramsey classes and homogeneous structures, Combin. Probab. Comput. 14 (2005), 171-189.10.1017/S0963548304006716Suche in Google Scholar
[22] ROSE, S. E.: Classification of Countable Homogeneous 2-Graphs. PhD Thesis, University of Leeds, 2011. Suche in Google Scholar
© Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Complexities of Relational Structures
- Notes on the Product of Locales
- Free Objects and Free Extensions in the Category of Frames
- More on Uniform Paracompactness in Pointfree Topology
- Nonmeasurable Cardinals and Pointfree Topology
- Pseudocompact σ-Frames
- Torsion Radicals and Torsion Classes of Cyclically Ordered Groups
- Generalized Commutativity of Lattice-Ordered Groups
- The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups
- Polymorphism-Homogeneous Monounary Algebras
- αcc-Baer Rings
- Pushout Invariance Revisited
- Testing Statistical Hypotheses in Singular Weakly Nonlinear Regression Models
Artikel in diesem Heft
- Complexities of Relational Structures
- Notes on the Product of Locales
- Free Objects and Free Extensions in the Category of Frames
- More on Uniform Paracompactness in Pointfree Topology
- Nonmeasurable Cardinals and Pointfree Topology
- Pseudocompact σ-Frames
- Torsion Radicals and Torsion Classes of Cyclically Ordered Groups
- Generalized Commutativity of Lattice-Ordered Groups
- The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups
- Polymorphism-Homogeneous Monounary Algebras
- αcc-Baer Rings
- Pushout Invariance Revisited
- Testing Statistical Hypotheses in Singular Weakly Nonlinear Regression Models
