 Thus, they claim that theoretical equivalence in MSL is to have a common Morita extension (this is called “Morita equivalence”). It is worth recalling at this point that the Morita extension \(T^{+}\) of \(T\) might be constructed by adding new sort symbols to the signature of \(T\) together with the corresponding explicit  definitions[33]  to the axioms. There are several ways to carry out this extension: the new sort \(\tau\) can be introduced as a subsort, product, coproduct and quotient sort (see Barrett &amp; Halvorson 2016: 563–64). Morita equivalence has also been used to try to clarify what is known in the literature as Quine’s conjecture on many-sorted logic (see Barrett &amp; Halvorson 2017).