Maximal hyperbolic towers and weight in the theory of free groups-Reference-Cited by-同舟云学术

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Maximal hyperbolic towers and weight in the theory of free groups

Published:2019-11-18 Issue:3 Volume:170 Page:479-498
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

BRÜCK BENJAMIN

Abstract

AbstractWe show that in general for a given group the structure of a maximal hyperbolic tower over a free group is not canonical: we construct examples of groups having hyperbolic tower structures over free subgroups which have arbitrarily large ratios between their ranks. These groups have the same first order theory as non-abelian free groups and we use them to study the weight of types in this theory.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference18 articles.

1. Valuations, Trees, and Degenerations of Hyperbolic Structures, I

2. On the generic type of the free group

3. Elementary theory of free non-abelian groups

4. [She78] Shelah, S. . Classification theory and the number of nonisomorphic models. Studies in Logic and the Foundations of Mathematics, vol. 92. (North-Holland Publishing Co., Amsterdam-New York, 1978).

5. Diophantine geometry over groups. VI. The elementary theory of a free group;Sela;Geom. Funct. Anal,2006

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