6 problems

For each $n\in\omega$, let $b_{2n+1,0}$ denote the cardinal invariant defined in the source from the direct-limit images of the relevant iterates of $M_{2n+1}(x)$, and let…

Let $n\in\omega$. A cardinal is $\bf{\Gamma}$-reachable if there is a sequence of distinct $\bf{\Gamma}$-sets of that length, and is $\bf{\Gamma}$-unreachable otherwise. Kechris pr…

Let $\lambda$ be a cardinal with $\bf{\delta^1_4}\leq\lambda\leq\bf{\delta^1_6}$, and suppose $\operatorname{cof}(\lambda)>\omega$. A cardinal is $\bf{\Gamma}$-unreachable when the…

Let $\bf{\Gamma}$ be a pointclass, and let $\kappa$ be $\bf{\Gamma}$-reachable when there is a sequence of distinct $\bf{\Gamma}$-sets of length $\kappa$; otherwise, $\kappa$ is…

Separation conjecture at intermediate projective levels. In the model $\rL[G\res\Da_H]$, the separation theorem holds for $\fp1m$ and fails for $\fs1m$ for every $m$ satisfying…

Projective-domain extension conjecture. It is consistent with ZFC that the domain in this theorem can be allowed to be $\boldsymbol{\Sigma}^1_2$, and possibly any other level of th…