Welcome to MathOverflow

Question

4

1

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?

flag	asked Mar 14 2012 at 15:56 Ajdin Halilovic 43●2

1

What is $TP(\omega_2)$? – Andreas Blass Mar 14 2012 at 18:36

1

It would seem to be the tree property: every $\omega_2$-tree has an $\omega_2$-branch. – Joel David Hamkins Mar 14 2012 at 22:15

Yes, I meant the tree property, sorry! – Ajdin Halilovic Mar 15 2012 at 11:36

Péter Komjáth · Accepted Answer · 2012-03-15 14:49:52Z UTC

7

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/).

answered Mar 15 2012 at 14:49

Péter Komjáth
3,428●13●19

Thank you very much for the answer! – Ajdin Halilovic Mar 15 2012 at 15:03

TP($\omega_2$) and the continuum

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.