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.
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Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
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Illustrationen
tables, bibliography, index
ISBN-13
978-3-540-64882-6 (9783540648826)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Pennsylvania State University, University Park, USA
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.
