Subsystems of Second Order Arithmetic (Perspectives in Mathematical Logic)

Simpson, Stephen G.

ISBN 10: 3540648828 / ISBN 13: 9783540648826

Published by Springer, 1999

Like New. Seller Inventory # ERICA75835406488286

Synopsis:

This volume focuses on the role of set existence axioms. Part A demonstrates that many familiar theorems of algebra, analysis, functional analysis, and combinatorics are logically equivalent to the axioms needed to prove them. This phenomenon is known as reverse mathematics. Subsystems of second order arithmetic based on such axioms correspond to several foundational programs: finitistic reductionism (Hilbert); constructivism (Bishop); predictavism (Weyl); and predictive reductionism (Feferman/Friedman). Part B is a thorough study of models of these and other systems.

Book Description: What are the appropriate axioms for mathematics? Through a series of case studies, this volume examines these axioms to prove particular theorems in core areas including 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.

Bibliographic Details

Title: Subsystems of Second Order Arithmetic (...
Publisher: Springer
Publication Date: 1999
Binding: Hardcover
Condition: Like New
Book Type: book