  We compare three notions of effectiveness on uncountable structures. The
first notion is that of a $\real$-computable structure, based on a model of
computation proposed by Blum, Shub, and Smale, which uses full-precision real
arithmetic. The second notion is that of an $F$-parameterizable structure,
defined by Morozov and based on Mal'tsev's notion of a constructive structure.
The third is $\Sigma$-definability over $HF(\real)$, defined by Ershov as a
generalization of the observation that the computably enumerable sets are
exactly those $\Sigma_1$-definable in $HF(\mathbb{N})$.
  We show that every $\real$-computable structure has an $F$-parameterization,
but that the expansion of the real field by the exponential function is
$F$-parameterizable but not $\real$-computable. We also show that the
structures with $\real$-computable copies are exactly the structures with
copies $\Sigma$-definable over $HF(\real)$. One consequence of this equivalence
is a method of approximating certain $\real$-computable structures by Turing
computable structures.
