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A Nonstandard Delta Function in a Predicative Theory

✍ Scribed by Peter Zahn

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 191 KB
Volume: 41
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19950410211

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✦ Synopsis

Abstract

In [1] Todorov has shown by means of axiomatic set theory that there exists a nonstandard function Δ: *ℝ^n^ → * ℂ such that for all continuous functions φ: ℝ^n^ → ℂ,
equation image
.

Here *ℝ and *ℂ are the set of the nonstandard real numbers and the set of the nonstandard complex numbers, respectively, and *φ: *ℝ^n^ → *ℂ is the nonstandard extension of φ In the present note we want to prove an analogous theorem by predicative means only.

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