A combinatorial proof of the extension property for partial isometries

Jan Hubička; Matěj Konečný; Jaroslav Nešetřil

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 1, page 39-47
  • ISSN: 0010-2628

Abstract

top
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.

How to cite

top

Hubička, Jan, Konečný, Matěj, and Nešetřil, Jaroslav. "A combinatorial proof of the extension property for partial isometries." Commentationes Mathematicae Universitatis Carolinae 60.1 (2019): 39-47. <http://eudml.org/doc/294542>.

@article{Hubička2019,
abstract = {We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.},
author = {Hubička, Jan, Konečný, Matěj, Nešetřil, Jaroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {metric space; Hrushovski property; extension property for partial automorphisms; homogeneous structure; amalgamation class},
language = {eng},
number = {1},
pages = {39-47},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A combinatorial proof of the extension property for partial isometries},
url = {http://eudml.org/doc/294542},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Hubička, Jan
AU - Konečný, Matěj
AU - Nešetřil, Jaroslav
TI - A combinatorial proof of the extension property for partial isometries
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 1
SP - 39
EP - 47
AB - We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
LA - eng
KW - metric space; Hrushovski property; extension property for partial automorphisms; homogeneous structure; amalgamation class
UR - http://eudml.org/doc/294542
ER -

References

top
  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. 
  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. 
  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. 
  4. Hall M. Jr., 10.1090/S0002-9947-1949-0032642-4, Trans. Amer. Math. Soc. 67 (1949), 421–432. MR0032642DOI10.1090/S0002-9947-1949-0032642-4
  5. Herwig B., Lascar D., 10.1090/S0002-9947-99-02374-0, Trans. Amer. Math. Soc. 352 (2000), no. 5, 1985–2021. MR1621745DOI10.1090/S0002-9947-99-02374-0
  6. Hodkinson I., Finite model property for guarded fragments, 2012, slides available at http://www.cllc.vuw.ac.nz/LandCtalks/imhslides.pdf. 
  7. Hodkinson I., Otto M., 10.2178/bsl/1058448678, Bull. Symbolic Logic 9 (2003), no. 3, 387–405. MR2005955DOI10.2178/bsl/1058448678
  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. 
  9. Hubička J., Konečný M., Nešetřil J., Conant's generalised metric spaces are Ramsey, available at arXiv:1710.04690 [math.CO] (2017), 22 pages. 
  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. 
  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. 
  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. 
  13. Konečný M., Semigroup-valued Metric Spaces, Master thesis in preparation available at arXiv:1810.08963 [math.CO], 2018. 
  14. Mackey G. W., 10.1007/BF01361167, Math. Ann. 166 (1966), no. 3, 187–207. MR0201562DOI10.1007/BF01361167
  15. Nešetřil J., 10.1016/j.ejc.2004.11.003, European J. Comb. 28 (2007), no. 1, 457–468. MR2261831DOI10.1016/j.ejc.2004.11.003
  16. Nešetřil J., Rödl V., 10.1090/S0002-9904-1977-14212-2, Bull. Amer. Math. Soc. 83 (1977), no. 1, 127–128. MR0422035DOI10.1090/S0002-9904-1977-14212-2
  17. Otto M., Amalgamation and symmetry: From local to global consistency in the finite, available at arXiv:1709.00031 [math.CO] (2017), 49 pages. 
  18. Pestov V. G., 10.1016/j.topol.2008.03.002, Topology Appl. 155 (2008), no. 14, 1561–1575. MR2435149DOI10.1016/j.topol.2008.03.002
  19. Rosendal Ch., 10.2178/jsl/1318338850, J. Symbolic Logic 76 (2011), no. 4, 1297–1306. MR2895386DOI10.2178/jsl/1318338850
  20. Ribes L., Zalesskii P. A., 10.1112/blms/25.1.37, Bull. London Math. Soc. 25 (1993), no. 1, 37–43. MR1190361DOI10.1112/blms/25.1.37
  21. Sabok M., Automatic continuity for isometry groups, J. Inst. Math. Jussieu (online 2017), 30 pages. MR3936642
  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. 
  23. Solecki S., 10.1007/BF02762385, Israel J. Math. 150 (2005), no. 1, 315–331. MR2255813DOI10.1007/BF02762385
  24. Solecki S., Notes on a strengthening of the Herwig–Lascar extension theorem, available at http://www.math.uiuc.edu/ssolecki/papers/HervLascfin.pdf (2009), 16 pages. 
  25. Vershik A. M., 10.1016/j.topol.2008.03.007, Topology Appl. 155 (2008), no. 14, 1618–1626. MR2435153DOI10.1016/j.topol.2008.03.007

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.