Scott, the best way to think of sharps is via mice. Think of $x^\#$ as a mouse over $x$ with one measure which is iterable. $\mathbb R^\#$ is a mouse over $\mathbb R$ with one measure which is iterable. Things become very easy ones you make the move from sharps as reals or sets of reals or etc to sharps as mice.
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Seeing how this question was bumped anyway, might as well LaTeX this answer up.
Asaf Karagila ♦
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Grigor
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