Consider ${\bf Z}$ as a first-order structure in the language $(0, +, -)$ of Abelian groups.
Which elements of ${\bf Z}$ are definable without parameters?
I think only 0 is, because there is no way to distinguish between x and -x.
Which elements of ${\bf Z}$ are definable without parameters in ${\bf Z}$?
3
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logic
model-theory
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3You are of course correct. The mapping $x \mapsto -x$ is an automorphism of $\mathbf{Z}$. – 2017-02-11
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3@user414998 You should just post that as an answer . . . – 2017-02-11