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Proceedings of the American Mathematical Society

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A purely algebraic characterization of the hyperreal numbers


Authors: Vieri Benci and Mauro Di Nasso
Journal: Proc. Amer. Math. Soc. 133 (2005), 2501-2505
MSC (2000): Primary 16S60, 54C40, 26E35
DOI: https://doi.org/10.1090/S0002-9939-05-07429-0
Published electronically: April 19, 2005
MathSciNet review: 2146232
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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.


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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: https://doi.org/10.1090/S0002-9939-05-07429-0
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
Published electronically: April 19, 2005
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2005 American Mathematical Society