New posts in Inner Model Theory

Does $0^{\#}$ imply the failure of upward directedness in the set generic universe over $L$?

Taking a proper class as a model for Set Theory

Reals which must, can't or might be added by forcing

Showing that $\alpha$ isn't a cardinal in $J_{\alpha+1}^{\vec E}$ for a fine extender sequence $\vec E$

Is it inconsistent for a model of set theory to contain its own first order theory?

Consistency strength of being strong cardinal and indestructible under collapses