  A natural framework for real-time specification is monadic first-order logic
over the structure $(\mathbb{R},<,+1)$---the ordered real line with unary $+1$
function. Our main result is that $(\mathbb{R},<,+1)$ has the 3-variable
property: every monadic first-order formula with at most 3 free variables is
equivalent over this structure to one that uses 3 variables in total. As a
corollary we obtain also the 3-variable property for the structure
$(\mathbb{R},<,f)$ for any fixed linear function
$f:\mathbb{R}\rightarrow\mathbb{R}$. On the other hand, we exhibit a countable
dense linear order $(E,<)$ and a bijection $f:E\rightarrow E$ such that
$(E,<,f)$ does not have the $k$-variable property for any $k$.
