jacket, Reverse Mathematics

Reverse Mathematics Proofs from the Inside Out

Hardback (09 Jan 2018) | English

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Synopsis

This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis-finding the "right axioms" to prove fundamental theorems-and giving a novel approach to logic.

Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it.

By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.

About the Publisher

Princeton University Press

Princeton University Press

We seek to publish the innovative works of the greatest minds in academia, from the most respected senior scholar to the extraordinarily promising graduate student, in each of the disciplines in which we publish. The Press consciously acquires a collection of titles--a coherent "list" of books--in each discipline, providing focus, continuity, and a basis for the development of future publications.

Book information

ISBN: 9780691177175
Publisher: Princeton University Press
Imprint: Princeton University Press
Pub date:
DEWEY: 511.3
DEWEY edition: 23
Language: English
Number of pages: xiii, 182
Weight: 494g
Height: 166mm
Width: 247mm
Spine width: 21mm