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Archive for Mathematical Logic

, Volume 57, Issue 7–8, pp 795–807 | Cite as

Homomorphism reductions on Polish groups

  • Konstantinos A. BerosEmail author
Article
  • 25 Downloads

Abstract

In an earlier paper, we introduced the following pre-order on the subgroups of a given Polish group: if G is a Polish group and \(H,L \subseteq G\) are subgroups, we say H is homomorphism reducible to L iff there is a continuous group homomorphism \(\varphi : G \rightarrow G\) such that \(H = \varphi ^{-1} (L)\). We previously showed that there is a \(K_\sigma \) subgroup L of the countable power of any locally compact Polish group G such that every \(K_\sigma \) subgroup of \(G^\omega \) is homomorphism reducible to L. In the present work, we show that this fails in the countable power of the group of increasing homeomorphisms of the unit interval.

Keywords

Polish groups Homomorphism reductions \(K_{\sigma }\) subgroups 

Mathematics Subject Classification

03E15 54H11 22A05 57S05 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Miami UniversityOxfordUSA

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