Since the continuum has to be a regular/singular uncountable cardinal, and since by Easton Theorem it can be anything we want it to be, what is the forcing that makes the continuum a weakly compact cardinal? 


If we can do that then $2^{\aleph\_0}$ will have the tree property. But I have to find out first what is the forcing that can make $2^{\aleph\_0}$ have the partition property $\kappa \to \(\kappa)^2$ i.e the forcing has to ensure that among the subsets that are added to $2^{\aleph\_0}$ we have some $H \subset 2^{\aleph\_0}$ of order type $2^{\aleph\_0}$ such that $F: $[$2^{\aleph\_0}$]$^2 \to 2$ is constant on $[H]^2$ for every such $F$. How do we get such an $H$?



How can I force the continuum to be weakly compact?
The continuum can't be weak compact. The continuum can't be a strong limit (basically by definition of a strong limit) and weak compact cardinals are always strong limits.


You could start with a weakly compact cardinal in the ground model and make it the continuum by your favorite way of changing the continuum, but by the above you'll destroy the weak compactness. (Under the assumption that weak compacts are consistent, of course.)


If you are just interested in getting the continuum to have the tree property, this is done in Mitchell's [Aronszajn trees and the independence of the transfer property](http://www.sciencedirect.com/science/article/B6X2C-46V007P-59/2/1ae14176e718107af20fac6b2e72b34b) by collapsing a weak compact to $\omega\_2$.


