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An example of a non non-archimedean Polish group with ample generics

Author: Maciej Malicki
Journal: Proc. Amer. Math. Soc. 144 (2016), 3579-3581
MSC (2010): Primary 03E15, 54H11
Published electronically: March 30, 2016
MathSciNet review: 3503726
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Abstract: For an analytic $ P$-ideal $ I$ we denote by $ S_I$ the Polish group of all the permutations of $ \mathbbm {N}$ with support in $ I$, equipped with a topology given by the corresponding submeasure on $ I$. We show that if $ \mbox {Fin} \subsetneq I$, then $ S_I$ has ample generics. This implies that there exists a non non-archimedean Polish group with ample generics.

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Additional Information

Maciej Malicki
Affiliation: Department of Mathematics and Mathematical Economics, Warsaw School of Economics, al. Niepodleglosci 162, 02-554,Warsaw, Poland

Keywords: Ample generics, non-archimedean groups, $P$-ideals
Received by editor(s): March 17, 2015
Received by editor(s) in revised form: October 23, 2015
Published electronically: March 30, 2016
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2016 American Mathematical Society

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