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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.
List of contents
Walks on Countable Ordinals.- Metric Theory of Countable Ordinals.- Coherent Mappings and Trees.- The Square-bracket Operation on Countable Ordinals.- General Walks and Their Characteristics.- Square Sequences.- The Oscillation Mapping and the Square-bracket Operation.- Unbounded Functions.- Higher Dimensions.
Summary
The walks on ordinals and analysis of their characteristics is a subject matter started by the author some twenty years ago in order to disprove a particular extension of the Ramsey theorem. A further analysis has shown however that the resulting method is quite useful in detecting critical mathematical objects in contexts where only rough classifications are possible. Recently the method has led us to solutions to some other problems in a variety of disciplines such as for example a natural extension of the unconditional basic sequence problem from the Banach space theory or the famous L-space problem from topology. The book gives a careful and comprehensive account of the method and gathers many of these applications in a unified and comprehensive manner. It is the only full exposition of the method since its invention in the early 1980s.
