Nondefinability Results for Expansions of the Field of Real Numbers by the Exponential Function and by the Restricted Sine Function
Bianconi, Ricardo
J. Symbolic Logic, Tome 62 (1997) no. 1, p. 1173-1178 / Harvested from Project Euclid
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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 $x \not\in\lbrack -\pi,\pi\rbrack$.
Publié le : 1997-12-14
Classification:  03C40,  03C10 
@article{1183745373,
     author = {Bianconi, Ricardo},
     title = {Nondefinability Results for Expansions of the Field of Real Numbers by the Exponential Function and by the Restricted Sine Function},
     journal = {J. Symbolic Logic},
     volume = {62},
     number = {1},
     year = {1997},
     pages = { 1173-1178},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745373}
}

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, Tome 62 (1997) no. 1, pp.  1173-1178. http://gdmltest.u-ga.fr/item/1183745373/