Retracts of ultrahomogeneous structures in the context of Katětov functors

• Autorzy: Mašulović D.

Identyfikatory

DOI

10.1515/dema-2015-0041

• Konferencja: Proceedings of the AAA88 - 88th Workshop on General Algebra Editors for the Special Issue: Anna Romanowska, Jonathan D. H. Smith
• Języki publikacji: EN

Abstrakty

EN

In this paper, we characterize retracts of a wide class of Fraïssé limits using the tools developed in a recent paper by W. Kubiś and the present author, which we refer to as Katětov functors. This approach enables us to conclude that in many cases, a structure is a retract of a Fraïssé limit if and only if it is algebraically closed in the surrounding category.

Słowa kluczowe

EN

Fraisse limits; retract; Katetov functors

PL

limity Fraissea; retrakt; funktory Katetova

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 4
• Strony: 562--577
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Mašulović D.

• Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 3, 21000 Novi Sad, Serbia

Bibliografia

• [1] I. Ben Yaacov, The linear isometry group of the Gurarij space is universal. arXiv:1203. 4915v4.
• [2] D. Bilge, J. Melleray, Elements of finite order in automorphism groups of homogeneous structures, Contrib. Discret. Math. 8 (2013), 88–119.
• [3] P. J. Cameron, J. Nešetřil, Homomorphism-homogeneous relational structures, Combin. Probab. Comput. 15 (2006), 91–103.
• [4] I. Dolinka, A characterization of retracts in certain Fraíssé limits, Math. Log. Q. 58 (2012), 46–54.
• [5] R. Fraïssé, Sur certains relations qui généralisent l’ordre des nombres rationnels, C. R. Acad. Sci. Paris 237 (1953), 540–542.
• [6] M. Katétov, On universal metric spaces. General topology and its relations to modern analysis and algebra, VI (Prague, 1986), Res. Exp. Math., vol. 16, Heldermann, Berlin, 1988, 323–330.
• [7] W. Kubiś, Injective objects and retracts of Fraïssé limits, Forum Math. 27 (2013), 807–842.
• [8] W. Kubiś, D. Mašulović, Katetov functors. arXiv:1412.1850v2.
• [9] P. S. Urysohn, Sur un espace métrique universel, Bull. Math. Sci. 51 (1927), 43–64, 74–90.