An inner model proof of the strong partition property of \delta^2_1

We prove the strong partition property for \delta^2_1 using methods from inner model theory.Comment: submitte

Unreachability of Γ2n+1,m\bf{\Gamma_{2n+1,m}}

We find bounds for the maximal length of a sequence of distinct $\bf{\Gamma_{2n+1,m}}$-sets under $AD$ and show there is no sequence of distinct $\bf{\Gamma_{2n+1}}$-sets of length $\bf{\delta^1_{2n+3}}$. As a special case, there is no sequence of distinct $\bf{\Gamma_{1,m}}$-sets of length $\aleph_{m+2}$. These are the optimal results for the pointclasses $\bf{\Gamma_{2n+1}}$ and $\bf{\Gamma_{1,m}}$