7 problems

Sufficiency conjecture. c93-chain-condition universal Baireness suffices for the argument above, namely for proving that $0^{\#}$ exists.

Let $V$ be a model of … For a set of reals $A$ and a set-generic extension $V[G*H]$, write $A^{V[G]}$ and $A^{V[G*H]}$ for the interpretations of $A$ in the relevant extensions. Ge…

A pointclass of universally Baire sets of reals is called productive when it is closed under complements and projections, and its projections are absolute between set-generic exten…

Chang-type uB-powerset sealing conjecture. Moreover, the $\sf{Sealing}$ Theorem holds for $\mathsf{C-uBp}$ in $V[g]$.

Amenable powerset conjecture. We conjecture that ${{\sf{uBp}}}$ is the amenable powerset of ${{\sf{uB}}}$.

Model completeness conjecture. The theory of $L_\Theta(\mathsf{UB}^{\omega_1})$ is model complete for the signature

Let $bb$ be a cardinal that is a limit of Woodin cardinals and a limit of strong cardinals. A model of … is a model satisfying the Axiom of Determinacy together with the assertion…