Subsystems of Second Order Arithmetic (Perspectives in Mathematical Logic) by Stephen G. Simpson
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This book is an original contribution to the foundations of mathematics, with emphasis 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 well known foundational programs: finitistic reductionism (Hilbert), constructivism (Bishop), predicativism (Weyl), and predicative reductionism (Feferman/Friedman). Part B is a thorough study of models of these and other systems. The book includes an extensive bibliography and a detailed index.From reader reviews:
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