Book: Subsystems of Second Order Arithmetic

I am Stephen G. Simpson, a mathematics professor at Penn State University.

January 1999 - March 2001

My book Subsystems of Second Order Arithmetic is finished! It includes much material on reverse mathematics. It was published in January 1999 by Springer-Verlag with editorial help from the Association for Symbolic Logic. The length of the book is XIV + 445 pages. A list of typos is available.

To make this book less expensive, I did all of the typesetting myself, and I refused royalties. The ASL also agreed to forgo royalties, so the list price is only 98 German marks, i.e., 60 US dollars. In addition, ASL members are entitled to a 30 percent discount, so the book is well within reach of individual purchasers.

To order from Springer-Verlag New York, telephone 1-800-SPRINGER or fax 1-212-533-5587. If you are a member of the Association for Symbolic Logic, mention Promotion Code S206 to obtain the 30 percent discount.

Here is some information to help you decide to buy this book.

promotional material
table of contents: plain ASCII
front matter and chapter one: DVI, PDF, PS
review by John Burgess (PM): HTML, DVI, PDF, PS
review by Peter Cholak (JSL): PDF, PS
review by Qi Feng (RNFBST): text (GB), PDF, PS, translation
review by Jeffrey Ketland (BJPS): HTML, DVI, PDF, PS
review by Michael Moellerfeld (MR): HTML, DVI, PDF, PS
review by Roman Murawski (ZB): HTML, DVI, PDF, PS
review by David Madore (SMF - Gazette): PDF, PS

The review by Jeffrey Ketland has appeared in the British Journal for Philosophy of Science, Volume 52, No. 1, March 2001, pp. 191-195.

The review by David Madore has appeared in the Gazette des Mathematiciens, Societe Mathematique de France, Volume 125, July 2010, pp. 135-137.

Here are some related links.

recent research in subsystems of second order arithmetic.
(Note: This summary is current as of April 12, 2001. For recent developments, see below.)
a new book on reverse mathematics, in preparation.
open problems in reverse mathematics: HTML, DVI, PDF, PS.
my web page on foundations of mathematics.
my automated e-mail list for discussing foundations of mathematics.
my course on reverse mathematics.
my other publications.

April 11, 2001

Recently Springer-Verlag ran out of copies of Subsystems of Second Order Arithmetic. On the one hand, I am gratified that my book sold so well. On the other hand, I am disappointed that there is currently no way for students and scholars to purchase it. I am working on a plan to get it reprinted in the near future.

July 8, 2005

On June 30, 2005 I submitted Subsystems of Second Order Arithmetic, Second Edition, to the Association for Symbolic Logic, for publication in their book series Perspectives in Logic. It was accepted on August 9, 2005.

On September 19, 2003 the Association for Symbolic Logic accepted Reverse Mathematics 2001 for publication in their book series Lecture Notes in Logic. This is a volume of papers by various authors, edited by me, on subsystems of second order arithmetic and reverse mathematics. There have been massive production delays, but I am hoping the book will appear soon.

Additional information:

Reverse mathematics update (June 15, 2005).
Reverse mathematics -- a bibliographical update (June 30, 2005).
List of typographical errors in the first edition of Subsystems of Second Order Arithmetic: HTML, DVI, PDF, PS.
My papers, books, and lecture notes.

September 20, 2005

Reverse Mathematics 2001 has finally appeared. It is Volume 21 in the ASL's book series Lecture Notes in Logic, X + 401 pages. You may order on-line from A. K. Peters, Ltd. The price is 70 US dollars for hardback, 40 US dollars paperback, with a 20 percent discount for ASL members (use the discount code "ASLmember").

t20@psu.edu   /  20 September 2005