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Title: A combinatorial proof of the extension property for partial isometries (English)
Author: Hubička, Jan
Author: Konečný, Matěj
Author: Nešetřil, Jaroslav
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 60
Issue: 1
Year: 2019
Pages: 39-47
Summary lang: English
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Category: math
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Summary: We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces. (English)
Keyword: metric space
Keyword: Hrushovski property
Keyword: extension property for partial automorphisms
Keyword: homogeneous structure
Keyword: amalgamation class
MSC: 05E18
MSC: 20B27
MSC: 20F05
MSC: 22F50
MSC: 37B05
MSC: 54E35
idZBL: Zbl 07088824
idMR: MR3946663
DOI: 10.14712/1213-7243.2015.275
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Date available: 2019-05-13T07:45:36Z
Last updated: 2021-04-05
Stable URL: http://hdl.handle.net/10338.dmlcz/147673
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Reference: [1] Aranda A., Bradley-Williams D., Hubička J., Karamanlis M., Kompatscher M., Konečný M., Pawliuk M.: Ramsey Expansions of Metrically Homogeneous Graphs.available at arXiv:1707.02612 [math.CO], 2017.
Reference: [2] Evans D., Hubička J., Konečný M., Nešetřil J.: EPPA for two-graphs and antipodal metric spaces.available at arXiv:1812.11157 [math.CO] (2018), 13 pages.
Reference: [3] Evans D. M., Hubička J., Nešetřil J.: Ramsey properties and extending partial automorphisms for classes of finite structures.available at arXiv:1705.02379 [math.CO] (2017), 33 pages.
Reference: [4] Hall M. Jr.: Coset representations in free groups.Trans. Amer. Math. Soc. 67 (1949), 421–432. MR 0032642, 10.1090/S0002-9947-1949-0032642-4
Reference: [5] Herwig B., Lascar D.: Extending partial automorphisms and the profinite topology on free groups.Trans. Amer. Math. Soc. 352 (2000), no. 5, 1985–2021. MR 1621745, 10.1090/S0002-9947-99-02374-0
Reference: [6] Hodkinson I.: Finite model property for guarded fragments.2012, slides available at http://www.cllc.vuw.ac.nz/LandCtalks/imhslides.pdf.
Reference: [7] Hodkinson I., Otto M.: Finite conformal hypergraph covers and Gaifman cliques in finite structures.Bull. Symbolic Logic 9 (2003), no. 3, 387–405. MR 2005955, 10.2178/bsl/1058448678
Reference: [8] Huang J., Pawliuk M., Sabok M., Wise D.: The Hrushovski property for hypertournaments and profinite topologies.available at arXiv:1809.06435 [math.LO] (2018), 20 pages.
Reference: [9] Hubička J., Konečný M., Nešetřil J.: Conant's generalised metric spaces are Ramsey.available at arXiv:1710.04690 [math.CO] (2017), 22 pages.
Reference: [10] Hubička J., Konečný M., Nešetřil J.: All those EPPA classes (Strengthenings of the Herwig–Lascar theorem).available at arXiv:1902.03855 [math.CO] (2019), 27 pages.
Reference: [11] Hubička J., Nešetřil J.: All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms).available at arXiv:1606.07979 [math.CO] (2016), 59 pages.
Reference: [12] Hubička J., Nešetřil J.: Ramsey theorem for designs.The Ninth European Conf. on Combinatorics, Graph Theory and Applications (EuroComb 2017), Viena, 2017, Electronic Notes in Discrete Mathematics 61 (2017), 623–629.
Reference: [13] Konečný M.: Semigroup-valued Metric Spaces.Master thesis in preparation available at arXiv:1810.08963 [math.CO], 2018.
Reference: [14] Mackey G. W.: Ergodic theory and virtual groups.Math. Ann. 166 (1966), no. 3, 187–207. MR 0201562, 10.1007/BF01361167
Reference: [15] Nešetřil J.: Metric spaces are Ramsey.European J. Comb. 28 (2007), no. 1, 457–468. MR 2261831, 10.1016/j.ejc.2004.11.003
Reference: [16] Nešetřil J., Rödl V.: A structural generalization of the Ramsey theorem.Bull. Amer. Math. Soc. 83 (1977), no. 1, 127–128. MR 0422035, 10.1090/S0002-9904-1977-14212-2
Reference: [17] Otto M.: Amalgamation and symmetry: From local to global consistency in the finite.available at arXiv:1709.00031 [math.CO] (2017), 49 pages.
Reference: [18] Pestov V. G.: A theorem of Hrushovski-Solecki-Vershik applied to uniform and coarse embeddings of the Urysohn metric space.Topology Appl. 155 (2008), no. 14, 1561–1575. MR 2435149, 10.1016/j.topol.2008.03.002
Reference: [19] Rosendal Ch.: Finitely approximate groups and actions. Part I: The Ribes-Zalesskiĭ property.J. Symbolic Logic 76 (2011), no. 4, 1297–1306. MR 2895386, 10.2178/jsl/1318338850
Reference: [20] Ribes L., Zalesskii P. A.: On the profinite topology on a free group.Bull. London Math. Soc. 25 (1993), no. 1, 37–43. MR 1190361, 10.1112/blms/25.1.37
Reference: [21] Sabok M.: Automatic continuity for isometry groups.J. Inst. Math. Jussieu (online 2017), 30 pages. MR 3936642
Reference: [22] Siniora D., Solecki S.: Coherent extension of partial automorphisms, free amalgamation, and automorphism groups.available at arXiv:1705.01888v3 [math.LO] (2018), 29 pages.
Reference: [23] Solecki S.: Extending partial isometries.Israel J. Math. 150 (2005), no. 1, 315–331. MR 2255813, 10.1007/BF02762385
Reference: [24] Solecki S.: Notes on a strengthening of the Herwig–Lascar extension theorem.available at http://www.math.uiuc.edu/${\scriptstyle\mathtt \sim}$ssolecki/papers/HervLascfin.pdf (2009), 16 pages.
Reference: [25] Vershik A. M.: Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space.Topology Appl. 155 (2008), no. 14, 1618–1626. MR 2435153, 10.1016/j.topol.2008.03.007
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