The Ground Axiom states that the set-theoretic universe is not a set-forcing extension of an inner model. By Reitz, it is first-order expressible and easy to force over any given ZFC model with class-sized forcing, preserving large cardinals.

Woodin showed that his Ultimate-L axiom implies the Ground Axiom. It doesn't seem to be "built in" to the statement of Woodin's axiom, so it is a very interesting result.

In contrast, forcing axioms do not imply the ground axiom because of preservation theorems. For example, PFA is preserved by $\omega_2$-closed forcing.

Question: Are there other set theoretic principles (that are natural, simple, or interesting) that imply the Ground Axiom, without being obviously designed to do so? Examples of non-fine-structural statements would be most interesting.

The Ground Axiom states that the set-theoretic universe is not a set-forcing extension of an inner model. By Reitz, it is first-order expressible and easy to force over any given ZFC model with class-sized forcing, preserving large cardinals.

Woodin showed that his Ultimate-L axiom implies the Ground Axiom. It doesn't seem to be "built in" to the statement of Woodin's axiom, so it is a very interesting result.

In contrast, forcing axioms do not imply the ground axiom because of preservation theorems. For example, PFA is preserved by $\omega_2$-closed forcing.

Question: Are there other set theoretic principles (that are natural, simple, or interesting) that imply the Ground Axiom, without being obviously designed to do so? Examples of non-fine-structural statements would be most interesting.