The tree property and the continuum function below aleph_omega

Abstrakt

We say that a regular cardinal $\kappa$, $\kappa> \aleph_0$, has the tree property if there are no $\kappa$-Aronszajn trees; we say that $\kappa$ has the weak tree property if there are no special $\kappa$-Aronszajn trees. Starting with infinitely many weakly compact cardinals, we show that the tree property at every even cardinal $\aleph_{2n}$, $0\aleph_{2n+1}$, $n \aleph_{n+1}$, $n\kappa^+$ for every infinite $\kappa$.

Klíčová slova

• tree property
• continuum function