Subsystems of second order arithmetic
Author(s)
Bibliographic Information
Subsystems of second order arithmetic
(Perspectives in mathematical logic)
Springer-Verlag, c1999
- : hard
Available at / 30 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardSIM||29||198051482
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: hardDC21:511.3/SI532070466072
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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"