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Nonstandard Analysis, Axiomatically (Springer Monographs in Mathematics) - Hardcover

Book 26 of 187: Springer Monographs in Mathematics

Kanovei, Vladimir; Reeken, Michael

 
9783540222439: Nonstandard Analysis, Axiomatically (Springer Monographs in Mathematics)
Hardcover
ISBN 10: 354022243X ISBN 13: 9783540222439
Publisher: Springer, 2004

Synopsis

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.

"synopsis" may belong to another edition of this title.

About the Author

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.

 

 

From the Back Cover

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 this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2004
Language
English
ISBN 10 
354022243X
ISBN 13 
9783540222439
Binding
Hardcover
Number of pages
410