FOM: new book: Subsystems of Second Order Arithmetic
Stephen G Simpson
simpson at math.psu.edu
Sun Jul 5 22:16:14 EDT 1998
Dear FOM subscribers,
I have just finished writing my long-awaited book "Subsystems of
Second Order Arithmetic"! It will be published later this year by
Springer-Verlag. The length of the book will be approximately 450
pages and the list price will be only 60 US dollars. Members of the
Association for Symbolic Logic will receive a 30 percent discount off
list, so the book will be well within reach of individual purchasers.
Here is my 100-word description of the book:
This book is an original contribution to 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.
More information about the book is at
including a PostScript file of the table of contents and chapter one.
Best regards to all,
Name: Stephen G. Simpson
Position: Professor of Mathematics
Institution: Penn State University
Research interest: foundations of mathematics
More information: www.math.psu.edu/simpson/
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