Walks on Ordinals and Their Characteristics

Stevo Todorcevic (auth.)3764385286, 978-3-7643-8528-6

The analysis of the characteristics of walks on ordinals is a powerful new technique for building mathematical structures, developed by the author over the last twenty years. This is the first book-length exposition of this method. Particular emphasis is placed on applications which are presented in a unified and comprehensive manner and which stretch across several areas of mathematics such as set theory, combinatorics, general topology, functional analysis, and general algebra. The intended audience for this book are graduate students and researchers working in these areas interested in mastering and applying these methods.

Table of contents :
Front Matter….Pages i-vi
Introduction….Pages 1-18
Walks on Countable Ordinals….Pages 19-53
Metric Theory of Countable Ordinals….Pages 55-90
Coherent Mappings and Trees….Pages 91-132
The Square-bracket Operation on Countable Ordinals….Pages 133-160
General Walks and Their Characteristics….Pages 161-185
Square Sequences….Pages 187-231
The Oscillation Mapping and the Square-bracket Operation….Pages 233-269
Unbounded Functions….Pages 271-288
Higher Dimensions….Pages 289-312
Back Matter….Pages 313-324