Solution

Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 19 / 4 / i / c / Solution

{title2=$\forall q\ge p\ \exists r\ge q\ (r\in D)$}

For the convention that larger conditions are stronger, density above $p$ means every strengthening of $p$ has a further strengthening in $D$. It is the extension-cone density usually called <dense below a forcing condition> when smaller conditions are stronger. The sign must be translated with the order convention, rather than copied unchanged.

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 Incoming links: Dense above a forcing condition