The Journal of Symbolic Logic

Research Article

Nondefinability results for expansions of the field of real numbers by the exponential function and by the restricted sine function

Ricardo Bianconi

IME-USP, Caixa Postal 66281, Cep 05389-970, São Paulo, SP, Brazil, E-mail: bianconi@ime.usp.br

Abstract

We prove that no restriction of the sine function to any (open and nonempty) interval is definable in 〈R, +, ·, ×, <, exp, constants〉, and that no restriction of the exponential function to an (open and nonempty) interval is definable in 〈R, +, ·, <, sin0, constants〉, where sin0(x) = sin(x) for x ∈ [—π, π], and sin0(x) = 0 for all x ∉ [—π, π].

(Received September 04 1995)

(Revised December 15 1995)