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 to...

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Simpson, Stephen G. 1945- (VerfasserIn)
Format:	Elektronisch Tagungsbericht E-Book
Sprache:	English
Veröffentlicht:	Cambridge Cambridge University Press 2009
Ausgabe:	Second edition
Schriftenreihe:	Perspectives in logic
Schlagworte:	Predicate calculus Axiomatik Mathematik Mathematische Logik Grundlage
Online-Zugang:	BSB01 FHN01 Volltext
Zusammenfassung:	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
Beschreibung:	Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Beschreibung:	1 online resource (xvi, 444 pages)
ISBN:	9780511581007
DOI:	10.1017/CBO9780511581007