## Journal of Symbolic Logic

### Nondefinability Results for Expansions of the Field of Real Numbers by the Exponential Function and by the Restricted Sine Function

Ricardo Bianconi

#### Abstract

We prove that no restriction of the sine function to any (open and nonempty) interval is definable in $\langle\mathbf{R}, +, \cdot, <, \exp, \text{constants}\rangle$, and that no restriction of the exponential function to an (open and nonempty) interval is definable in $\langle \mathbf{R}, +, \cdot, <, \in_0, \text{constants}\rangle$, where $\sin_0(x) = \sin(x)$ for $x \in \lbrack -\pi,\pi\rbrack$, and $\sin_0(x) = 0$ for all $x \not\in\lbrack -\pi,\pi\rbrack$.

#### Article information

Source
J. Symbolic Logic, Volume 62, Issue 4 (1997), 1173-1178.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745373

Mathematical Reviews number (MathSciNet)
MR1617985

Zentralblatt MATH identifier
0899.03026

JSTOR

#### Citation

Bianconi, Ricardo. Nondefinability Results for Expansions of the Field of Real Numbers by the Exponential Function and by the Restricted Sine Function. J. Symbolic Logic 62 (1997), no. 4, 1173--1178. https://projecteuclid.org/euclid.jsl/1183745373