#-generated reflection, or Indiscernible-generation, is considered to be the strongest reflection principle that does not violate the covering lemma in L. [1]
Is there a way to extend this success to other inner/core models has covering lemmas proofs? (like $L(R), L[U], ...$)
[1] Friedman, S.-D. and Honzik, R. (2016), "On strong forms of reflection in set theory". Math. Log. Quart., 62: 52-58, DOI:10.1002/malq.201400047, MR3472179, Zbl 1357.03084.
