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