 Nevertheless, according to Mceldowney (2020), a nuanced concept of Morita equivalence is just a special case of bi-interpretability. For this reason, he opted for a notion of equivalence in MSL based on interpretability rather than Morita extensions (see pp. 404-407 in Mceldowney 2020). In fact, as pointed out in Friedman and Visser (2014), bi-interpretability preserves finite axiomatizability, decidability, and κ-categoricity.