Abstract
Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis proposed around 1995 by Chuaqui, Suppes and Sommer. It has been shown to be consistent and, without standard part function or continuum, it allows major parts of analysis to be developed in an applicable form. We briefly discuss ERNA’s foundations and use them to prove a supremum principle and provide a square root function, both up to infinitesimals.
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References
R. Chuaqui and P. Suppes, “Free-Variable Axiomatic Foundations of Infinitesimal Anaysis: A Fragment with Finitary Consistency Proof”, J. Symb. Logic, 60 (1995) 122–159.
R. Sommer and P. Suppes, “Finite Models of Elementary Recursive Nonstandard Analysis”, Notas de la Sociedad Matematica de Chile, 15 (1996) 73–95.
R. Sommer and P. Suppes, “Dispensing with the Continuum”, J. Math. Psychology, 41 (1997) 3–10.
P. Suppes and R. Chuaqui, A finitarily consistent free-variable positive fragment of Infinitesimal Anaysis, Proceedings of the IXth Latin American Symposium on Mathematical Logic, Notas de Logica Mathematica, 38 (1993) 1–59, Universidad Nacional del Sur, Bahia Blanca, Argentina.
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© 2007 Springer-Verlag Wien
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Impens, C., Sanders, S. (2007). ERNA at work. In: van den Berg, I., Neves, V. (eds) The Strength of Nonstandard Analysis. Springer, Vienna. https://doi.org/10.1007/978-3-211-49905-4_5
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DOI: https://doi.org/10.1007/978-3-211-49905-4_5
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-49904-7
Online ISBN: 978-3-211-49905-4
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