John Stillwell 
Reverse Mathematics [PDF ebook] 
Proofs from the Inside Out

Support

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.

€21.99
payment methods

About the author

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. His many books include
Mathematics and Its History and
Elements of Mathematics: From Euclid to Gödel (Princeton).

Buy this ebook and get 1 more FREE!
Language English ● Format PDF ● Pages 200 ● ISBN 9781400889037 ● File size 2.9 MB ● Publisher Princeton University Press ● City Princeton ● Country US ● Published 2018 ● Downloadable 24 months ● Currency EUR ● ID 5481571 ● Copy protection Adobe DRM
Requires a DRM capable ebook reader

More ebooks from the same author(s) / Editor

943 Ebooks in this category

Franz Rothe: A Course in Old and New Geometry : Volume V
The present fifth volume  recalls Hilbert’s axioms from the Foundations of 
') jQuery('#virelinsocial').html('
'); jQuery('.virelinsocial-link').css('display','block').css('margin','0px').css('margin-bottom','5px'); jQuery('#virelinsocial').show(); }); // end of document ready // END wait until jQuery is available } }, 30); })();