FOM: new book: Subsystems of Second Order Arithmetic

Stephen G Simpson simpson at
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,
-- Steve

Name: Stephen G. Simpson
Position: Professor of Mathematics
Institution: Penn State University
Research interest: foundations of mathematics
More information:

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