Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Some model theory of Polish structures

Author: Krzysztof Krupinski
Journal: Trans. Amer. Math. Soc. 362 (2010), 3499-3533
MSC (2010): Primary 03C45, 03E15; Secondary 54H11, 20E18, 54F15
Published electronically: February 15, 2010
MathSciNet review: 2601598
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a notion of Polish structure and, in doing so, provide a setting which allows the application of ideas and techniques from model theory, descriptive set theory, topology and the theory of profinite groups. We define a topological notion of independence in Polish structures and prove that it has some nice properties. Using this notion, we prove counterparts of some basic results from geometric stability theory in the context of small Polish structures. Then, we prove some structural theorems about compact groups regarded as Polish structures: each small, $ nm$-stable compact $ G$-group is solvable-by-finite; each small compact $ G$-group of finite $ {\mathcal NM}$-rank is nilpotent-by-finite. Examples of small Polish structures and groups are also given.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 03C45, 03E15, 54H11, 20E18, 54F15

Retrieve articles in all journals with MSC (2010): 03C45, 03E15, 54H11, 20E18, 54F15

Additional Information

Krzysztof Krupinski
Affiliation: Instytut Matematyczny Uniwersytetu Wrocławskiego, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland – and – Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801

Keywords: Polish structure, Polish group, profinite group, independence relation
Received by editor(s): February 11, 2008
Published electronically: February 15, 2010
Additional Notes: This research was supported by the Polish Government grant N201 032 32/2231 and by NSF grant DMS 0300639
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia