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.

Only full exposition of the method since its invention in the early 1980s In recent times the method is finding remarkable new appplications Includes supplementary material: sn.pub/extras

Inhalt
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.