الصفحة 1
الصفحة 1
Walks on Ordinals and Their Characteristics
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.
Set Theory : Centre de Recerca Matemàtica Barcelona, 2003-2004
This volume has its origins in the Research Programme on Set Theory and its Applications that took place at the Centre de Recerca Matemática (CRM) Barcelona from September 2003 to July 2004. It consists of two parts. The first contains survey papers on some of the mainstream areas of set theory, and the second contains original research papers.
Ramsey Methods in Analysis
This book introduces graduate students and resarchers to the study of the geometry of Banach spaces using combinatorial methods. The combinatorial, and in particular the Ramsey-theoretic, approach to Banach space theory is not new, it can be traced back as early as the 1970s. Its full appreciation, however, came only during the last decade or so, after some of the most important problems in Banach space theory were solved, The book covers most of these advances, but one of its primary purposes is to discuss some of the recent advances that are not present in survey articles of these areas. We also apply the Nash-Williams theory of fronts and barriers in the study of Cezaro summability and unconditionality present in basic sequences inside a given Banach space. We further provide a detailed exposition of the block-Ramsey theory and its recent deep adjustments relevant to the Banach space theory due to Gowers.
