Reverse Mathematics: Proofs from the Inside Out
| Author | : | |
| Rating | : | 4.18 (896 Votes) |
| Asin | : | B073RSSMWG |
| Format Type | : | |
| Number of Pages | : | 260 Pages |
| Publish Date | : | 2017-08-26 |
| Language | : | English |
DESCRIPTION:
Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Thus arithmetic in some sense underlies analysis, logic, and computation. This book presents reverse mathematics to a general mathematical audience for the first time. 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. 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.. The second was the twentieth-century arithmetization of logic and computation. Reverse mathematics is a new field that answers some old questions. In Reverse Mathematics, John Stillwell gives a representative vi
I heartily commend this very readable and accessible book."--Stephen Simpson, Vanderbilt University. From the Back Cover"Filling an important niche, this book gives readers a good picture of the basics of reverse mathematics while suggesting several directions for further reading and study. Stillwell's book is self-contained and includes much background material in analysis, mathematical logic, combinatorics, and computability. It provides a context for the questions investigated by reverse mathematics an
His many books include Mathematics and Its History and Elements of Mathematics: From Euclid to Gödel (Princeton). John Stillwell is professor of mathematics at the University of San Francisco and an affiliate of the School of Mathematical Sciences at Monash University, Australia.