Random Walk: A Modern Introduction

Random Walk: A Modern Introduction


by Gregory F. Lawler; Vlada Limic

Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.

Cambridge University Press; June 2010 378 pages; ISBN 9780511741036 Read online , or download in secure PDF format Title: Random Walk: A Modern Introduction Author: Gregory F. Lawler; Vlada Limic   Buy, download and read Random Walk: A Modern Introduction (eBook) by Gregory F. Lawler; Vlada Limic today!
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