Easton's theorem for the tree property below aleph_omega

Abstract

Starting with infinitely many supercompact cardinals, we show that the tree property at every cardinal ${\aleph }_n$, $1<n<\omega$, is consistent with an arbitrary continuum function below ${\aleph }_{\omega }$ which satisfies $2^{{\aleph }_n}>{\aleph }_{n+1}$, $n<\omega$. Thus the tree property has no provable effect on the continuum function below ${\aleph }_{\omega }$ except for the restriction that the tree property at ${\kappa }^{++}$ implies $2^{\kappa }>{\kappa }^{+}$ for every infinite $\kappa$.

24 pages, submitted