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A purely algebraic characterization of the hyperreal numbers
Author(s):
Vieri
Benci;
Mauro
Di Nasso
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2501-2505.
MSC (2000):
Primary 16S60, 54C40, 26E35
Posted:
April 19, 2005
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Abstract:
The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.
References:
-
- 1.
- M.Y. Antonovskij, D.V. Chudnovsky, G.V. Chudnovsky and E. Hewitt, Rings of real-valued continuous functions. II, Math. Z. 176 (1981), 151-186. MR 0607959 (83f:54011)
- 2.
- V. Benci and M. Di Nasso, A ring homomorphism is enough to get nonstandard analysis, Bull. Belg. Math. Soc. - S. Stevin 10 (2003), 481-490. MR 2040525 (2004k:16084)
- 3.
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- 4.
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- 5.
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- 6.
- L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand, 1960. MR 0116199 (22:6994)
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- 9.
- J.J. Moloney, Residue class domains of the ring of convergent sequences and of
![$C^\infty([0,1],\mathbb{R} )$](/proc/2005-133-09/S0002-9939-05-07429-0/gif-references0/img1.gif) , Pacific J. Math. 143 (1990), 79-153. MR 1047403 (91k:12009) - 10.
- J. Roitman, Non-isomorphic hyper-real fields from non-isomorphic ultrapowers, Math. Z. 181 (1982), 93-96. MR 0671717 (84a:54030)
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Additional Information:
Vieri
Benci
Affiliation:
Dipartimento di Matematica Applicata ``Ulisse Dini'', Università di Pisa, Pisa, Italy
Email:
benci@dma.unipi.it
Mauro
Di Nasso
Affiliation:
Dipartimento di Matematica ``Leonida Tonelli'', Università di Pisa, Pisa, Italy
Email:
dinasso@dm.unipi.it
DOI:
10.1090/S0002-9939-05-07429-0
PII:
S 0002-9939(05)07429-0
Keywords:
Rings of functions,
algebraic properties of functions spaces,
nonstandard analysis
Received by editor(s):
November 13, 2002
Received by editor(s) in revised form:
July 11, 2003
Posted:
April 19, 2005
Communicated by:
Carl G. Jockusch, Jr.
Copyright of article:
Copyright
2005,
American Mathematical Society
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