Universality of group embeddability
作者： Filippo Calderoni , Luca Motto Ros
DOI: 10.1090/PROC/13857
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摘要: Working in the framework of Borel reducibility, we study various notions embeddability between groups. We prove that countable groups, topological (discrete) Polish and isometric separable groups with a bounded bi-invariant complete metric are all invariantly universal analytic quasi-orders. This strengthens some results from [Wil14] [FLR09].
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sci-hub.se 参考文章(13)
Itaï Ben Yaacov, Alexander Berenstein, C. Ward Henson, Alexander Usvyatsov, Model theory for metric structures Model Theory with Applications to Algebra and Analysis. pp. 315- 427 ,(2008) , 10.1017/CBO9780511735219.011
R. Rado, Universal graphs and universal functions Acta Arithmetica. ,vol. 9, pp. 331- 340 ,(1964) , 10.4064/AA-9-4-331-340
Christian Rosendal, Valentin Ferenczi, Alain Louveau, The complexity of classifying separable Banach spaces up to isomorphism Journal of The London Mathematical Society-second Series. ,vol. 79, pp. 323- 345 ,(2009) , 10.1112/JLMS/JDN068
Alain Louveau, Christian Rosendal, Complete analytic equivalence relations Transactions of the American Mathematical Society. ,vol. 357, pp. 4839- 4866 ,(2005) , 10.1090/S0002-9947-05-04005-5
Su Gao, Alexander S. Kechris, On the classification of Polish metric spaces up to isometry Memoirs of the American Mathematical Society. ,vol. 161, pp. 0- 0 ,(2003) , 10.1090/MEMO/0766
Harvey Friedman, Lee Stanley, A Borel Reducibility Theory for Classes of Countable Structures Journal of Symbolic Logic. ,vol. 54, pp. 894- 914 ,(1989) , 10.2307/2274750
Sy-David Friedman, Luca Motto Ros, Analytic equivalence relations and bi-embeddability Journal of Symbolic Logic. ,vol. 76, pp. 243- 266 ,(2011) , 10.2178/JSL/1294170999
Riccardo Camerlo, Alberto Marcone, Luca Motto Ros, Invariantly universal analytic quasi-orders Transactions of the American Mathematical Society. ,vol. 365, pp. 1901- 1931 ,(2012) , 10.1090/S0002-9947-2012-05618-2
Riccardo Camerlo, Alberto Marcone, Luca Motto Ros, On isometry and isometric embeddability between metric and ultrametric Polish spaces arXiv: Logic. ,(2014)
Marcin Sabok, Completeness of the isomorphism problem for separable C*-algebras Inventiones mathematicae. ,vol. 204, pp. 833- 868 ,(2016) , 10.1007/S00222-015-0625-5