Subsystems of second order arithmetic

Author(s)

• Simpson, Stephen G. (Stephen George)

Bibliographic Information

Subsystems of second order arithmetic

Stephen G. Simpson

（Perspectives in mathematical logic）

Springer-Verlag, c1999

• : hard

Note

Bibliography: p. [413]-424

Includes index

Description and Table of Contents

Description

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.

Table of Contents

• Part A Development of mathematics within subsystems of Z2: recursive comprehension
• arithmetical comprehension
• weak Konig's lemma
• arithmetical transfinite recursion
• pill comprehension. Part B Models of subsystems of Z2: beta-models
• omega-models
• non-omega models
• additional results.

by "Nielsen BookData"

Details

• NCID: BA38597577
• ISBN:
  • 3540648828
• LCCN: 98043371
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin ; Tokyo
• Pages/Volumes: xiv, 444 p.
• Size: 25 cm
• Classification:
  • LCC : QA9.7
  • DC21 : 511.3
• Subject Headings:
  • LCSH : Predicate calculus
• Parent Bibliography ID:
  • BA00027452