## Journal of Symbolic Logic

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

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

#### 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

**Permanent link to this document**

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

**Mathematical Reviews number (MathSciNet)**

MR1617985

**Zentralblatt MATH identifier**

0899.03026

**JSTOR**

links.jstor.org

**Subjects**

Primary: 03C40: Interpolation, preservation, definability

Secondary: 03C10: Quantifier elimination, model completeness and related topics

#### 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