Walks on Ordinals and Their CharacteristicsThe 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. |
Contents
| 1 | |
Walks on Countable Ordinals | 19 |
Metric Theory of Countable Ordinals | 55 |
Coherent Mappings and Trees | 91 |
The Squarebracket Operation on Countable Ordinals | 133 |
General Walks and Their Characteristics | 161 |
Square Sequences | 186 |
The Oscillation Mapping and the Squarebracket Operation | 233 |
Unbounded Functions | 270 |
Higher Dimensions | 289 |
| 313 | |
| 321 | |
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Common terms and phrases
antichain Applying assume assumption Banach space basic basis belongs bounded C-sequence cardinal characteristic Choose closed and unbounded cofinal coherent conclusion condition consider construction contains Corollary corresponding countable defined Definition denote elements equal equivalent example exist extends fact finishes finite subsets fixed forcing function given gives Going height hypothesis inductive inequality infinite integer interval isomorphic Lemma limit ordinal limit point minimal Moreover natural node nontrivial Note notion ordering oscillation pair pairwise-disjoint particular positive poſo projection proof prove Recall regular cardinal Remark restriction result satisfies sequence ſlo space square sequence square-bracket operation stationary set strictly increasing structure successor Suppose takes Theorem theory trace tree unbounded subset uncountable walk