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Cultures of Mathematics and Logic

by Thomas Müller Benedikt Löwe Shier Ju Yun Xie

This bookgathers the proceedings of the conference "Cultures of Mathematics andLogic," held in Guangzhou, China. The event was the third in a series ofinterdisciplinary, international conferences emphasizing the culturalcomponents of philosophy of mathematics and logic. It brought togetherresearchers from many disciplines whose work sheds new light on the diversityof mathematical and logical cultures and practices. In this context, thecultural diversity can be diachronical (different cultures in differenthistorical periods), geographical (different cultures in different regions), orsociological in nature.

A Universal Construction for Groups Acting Freely on Real Trees

by Ian Chiswell Thomas Müller

The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.

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