# 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.

Thanks in advance.

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

## 1 Answer

Shameless self-promotion: My chapter "Combinatorial cardinal characteristics of the continuum" in the Handbook of Set Theory, vol. 1, has this result in Section 11.3, at the bottom of page 472. You can download a version of the chapter from my web site at http://www.math.lsa.umich.edu/~ablass/hbk.pdf .

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Thank you for your helpful answer! :) – Rolfor Jan 31 '13 at 14:53