Walks on Ordinals and Their Characteristics Book

Introduction
Walks and the metric theory of ordinals     1
Summary of results     10
Prerequisites and notation     17
Acknowledgements     18
Walks on Countable Ordinals
Walks on countable ordinals and their basic characteristics     19
The coherence of maximal weights     29
Oscillations of traces     40
The number of steps and the last step functions     47
Metric Theory of Countable Ordinals
Triangle inequalities     55
Constructing a Souslin tree using [rho]     58
A Hausdorff gap from [rho]     63
A general theory of subadditive functions on [omega]     66
Conditional weakly null sequences based on subadditive functions     77
Coherent Mappings and Trees
Coherent mappings     91
Lipschitz property of coherent trees     95
The global structure of the class of coherent trees     108
Lexicographically ordered coherent trees     124
Stationary C-lines     128
The Square-bracket Operation on Countable Ordinals
The upper trace and the square-bracket operation     133
Projecting the square-bracket operation     139
Some geometrical applications of the square-bracket operation     144
Asquare-bracket operation from a special Aronszajn tree     152
A square-bracket operation from the complete binary tree     157
General Walks and Their Characteristics
The full code and its application in characterizing Mahlo cardinals     161
The weight function and its local versions     174
Unboundedness of the number of steps     178
Square Sequences
Square sequences and their full lower traces     187
Square sequences and local versions of [rho]     195
Special square sequence and the corresponding function [rho]     202
The function [rho] on successors of regular cardinals     205
Forcing constructions based on [rho]     213
The function [rho] on successors of singular cardinals     220
The Oscillation Mapping and the Square-bracket Operation
The oscillation mapping     233
The trace filter and the square-bracket operation     243
Projections of the square-bracket operation on accessible cardinals     251
Two more variations on the square-bracket operation     257
Unbounded Functions
Partial square-sequences     271
Unbounded subadditive functions     273
Chang's conjecture and [Theta subscript 2]     277
Higher dimensions and the continuum hypothesis      283
Higher Dimensions
Stepping-up to higher dimensions     289
Chang's conjecture as a 3-dimensional Ramsey-theoretic statement     294
Three-dimensional oscillation mapping     298
Two-cardinal walks     305
Bibliography     313
Index     321