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A Nonstandard Delta Function in a Predicative Theory
Author(s) -
Zahn Peter
Publication year - 1995
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19950410211
Subject(s) - predicative expression , mathematics , extension (predicate logic) , axiom , set (abstract data type) , function (biology) , discrete mathematics , pure mathematics , algebra over a field , computer science , geometry , evolutionary biology , biology , programming language , philosophy , linguistics
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,. 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.