# TP($\omega_2$) and the continuum

I think that in all classical models of TP($\omega_2$) we have $2^{\omega_0}=\omega_2$. Is there a known model of TP($\omega_2$) + $2^{\omega_0}>\omega_2$ at all?

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What is $TP(\omega_2)$? –  Andreas Blass Mar 14 '12 at 18:36
It would seem to be the tree property: every $\omega_2$-tree has an $\omega_2$-branch. –  Joel David Hamkins Mar 14 '12 at 22:15
Yes, I meant the tree property, sorry! –  Ajdin Halilovic Mar 15 '12 at 11:36

## 1 Answer

I think Spencer Unger in "Fragility and indestructibility of the tree property" proves that if one adds an arbitrary number of Cohen reals to Mitchell's model, then the tree property survives (see http://www.math.cmu.edu/~sunger/).

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Thank you very much for the answer! –  Ajdin Halilovic Mar 15 '12 at 15:03