A beautiful and surprising (to me at least) result around the axiom of choice is that, while full $\mathsf{AC}$ is preserved by forcing, a model of $\mathsf{ZF}$ + "There are no amorphous sets" may have a (set-)generic extension in which there do exist amorphous sets. This was proved by Monro, *On generic extensions without the axiom of choice*; see also Asaf Karagila's summary here.

I'm interested in not-too-strong sufficient conditions on a c.t.m. $\mathcal{M}\models\mathsf{ZF}$ to have no generic extensions in which amorphous sets exist. Specifically, I'm curious if the following model-theoretic condition does the job:

Say that a c.t.m. $\mathcal{M}\models\mathsf{ZF}$ is

expansiveiff for every first-order theory $T\in \mathcal{M}$ in a finite language with infinite models, every infinite set in $\mathcal{M}$ is the underlying set of a model of $T$ in $\mathcal{M}$.

*(Note that such an $\mathcal{M}$ does correctly compute whether such a $T$ has infinite models.)* For instance, expansiveness prevents the existence of infinite Dedekind-finite sets, since we can take $T$ to be the theory of a discrete linear order. My question, then, is how expansiveness, amorphousness in particular, and forcing interact:

Is every set-generic extension of an expansive c.t.m. also expansive?

If not, is there a set-generic extension of an expansive c.t.m. which has amorphous sets?

(Incidentally, it's not immediately clear to me that expansiveness is any stronger than "Infinite = Dedekind-infinite"!)

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