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New Examples of Small Polish Structures

Published online by Cambridge University Press:  12 March 2014

Jan Dobrowolski*
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, PL. Grunwaldzki 2/4, 50-384 Wrocław, Poland, E-mail: dobrowol@math.uni.wroc.pl

Abstract

We answer some questions from [4] by giving suitable examples of small Polish structures. First, we present a class of small Polish group structures without generic elements. Next, we construct a first example of a small non-zero-dimensional Polish G-group.

Keywords

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2013

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References

[1] Camerlo, R., Dendrites as polish structures, Proceedings of the American Mathematical Society, vol. 139 (2011), no. 6, pp. 22172225.CrossRefGoogle Scholar
[2] Dijkstra, J. J., A criterion for Erdös spaces, Proceedings of the Edinburgh Mathematical Society, vol. 48 (2005), pp. 595601.CrossRefGoogle Scholar
[3] Dijkstra, J. J., Van Mill, Jan, and Steprāns, Juris, Complete Erdös space is unstable, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 137 (2004), pp. 465473.CrossRefGoogle Scholar
[4] Krupiński, K., Some model theory of Polish structures, Transactions of the American Mathematical Society, vol. 362 (2010), pp. 34993533.CrossRefGoogle Scholar
[5] Krupiński, K. and Wagner, F., Small, nm-stable compact G-groups, Israel Journal of Mathematics, vol. 194 (2013), no. 2, pp. 907933.CrossRefGoogle Scholar
[6] Newelski, L., Small profinite groups, this Journal, vol. 66 (2001), pp. 859872.Google Scholar
[7] Newelski, L., Small profinite structures, Transactions of the American Mathematical Society, vol. 354 (2002), pp. 925943.CrossRefGoogle Scholar
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