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"From the point of view of the foundations of mathematics, this definitive work by Simpson is the most anxiously awaited monograph for over a decade. The "subsystems of second order arithmetic" provide the basic formal systems normally used in our current understanding of the logical structure of classical mathematics. Simpson provides an encyclopedic treatment of these systems with an emphasis on Hilbert's program (where infinitary mathematics is to be secured or reinterpreted by finitary mathematics), and the emerging reverse mathematics (where axioms necessary for providing theorems are determined by deriving axioms from theorems). The classical mathematical topics treated in these axiomatic terms are very diverse, and include standard topics in complete separable metric spaces and Banach spaces, countable groups, rings, fields, and vector spaces, ordinary differential equations, fixed points, infinite games, Ramsey theory, and many others. The material, with its many open problems and detailed references to the literature, is particularly valuable for proof theorists and recursion theorists. The book is both suitable for the beginning graduate student in mathematical logic, and encyclopedic for the expert." Harvey Friedman, Ohio State University.
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Previews available in: English
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1
Subsystems of Second Order Arithmetic
2010, Cambridge University Press
in English
0511581009 9780511581007
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2
Subsystems of Second-Order Arithmetic
2010, Cambridge University Press
in English
0521150140 9780521150149
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3
Subsystems of Second Order Arithmetic
2009, Cambridge University Press
in English
0511580681 9780511580680
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4
Subsystems of Second Order Arithmetic
2009, Cambridge University Press
in English
0511577273 9780511577277
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5
Subsystems of Second Order Arithmetic
2009, Cambridge University Press
in English
051157911X 9780511579110
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6
Subsystems of Second Order Arithmetic
1999, Springer Berlin Heidelberg
electronic resource /
in English
3642642039 9783642642036
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7
Subsystems of Second Order Arithmetic
Nov 05, 1998, Springer My Copy UK
paperback
3642599729 9783642599729
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