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Springer Monographs in Mathematics

Nonstandard Analysis, Axiomatically

Authors: Kanovei, Vladimir, Reeken, Michael

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About this book

In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan­ dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat­ ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.

About the authors

I) Vladimir Kanovei

graduated Moscow State university 1973
PhD Moscow State university 1976
Doctor of Science in Phys. Math. Moscow Steklov inst. 1986

assistant to full professor at Moscow Railroad engineering inst.
1976 - 1998

currently leading researcher at Institute for Information
transmissin problems (IITP) Moscow

interests in mathematics:
logic and foundations, set theory, nonstandard analysis
publications:
over 100 papers in Russian and international mathematical journals

II)
Michael Reeken
PhD in theoretical physics, University of Vienna 1968

Research Fellow at the Battelle Institute, Geneva, 1969 - 1972

Research grant at the University of Bonn, 1972 - 1974

Professor at the University of Bochum, 1972 - 1979

Full Professor at the Bergische Universität Wuppertal since 1979

interests in mathematics:
problems from mathematical physics, nonlinear functional analysis,
nonstandard mathematics, philosophy of mathematics.

 

 

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-662-08998-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
Softcover $109.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Nonstandard Analysis, Axiomatically
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-08998-9
DOI
10.1007/978-3-662-08998-9
Hardcover ISBN
978-3-540-22243-9
Softcover ISBN
978-3-642-06077-9
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XVI, 410
Topics