# 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.

EDIT: Actually, I found a proof in some lecture notes. I just need a reference to a paper where one can find the theorem.

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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
You're right, I changed it in the question. Thank you. –  Rolfor Jan 30 '13 at 17:49