# Why is the ground model set of reals nonmeager in the Cohen extension?

To be more precise, I want to add a Cohen real to a ground model $V$ of ZFC and then show that for each open interval $(a,b)$, the set $V \cap (a,b)$ is nonmeager in the extension.

Adding one is the same as adding $\omega$, so you might as well add just that one. – Asaf Karagila Jan 30 '13 at 17:44