So, we've been doing a lot of formalising of definite descriptions according to Russell, where we take the Definite Description as a predicate rather than designator.
So, I've formalised sentences like "The major of london ......" with this kind of predicate:
Mx: x is a major of London
But, my question is if I can formalise this even more?
On a recent test I, out of habit, made this key (because I was once told "the more we formalise, the better"):
Mxy: x is a major of y
But in hindsight I fear this may have been a mistake ...
I translated the sentence "The major of London is happy" as
$$ \exists x \Big(Mxl \land \forall y(Myl \rightarrow y=x) \land Hx \Big)$$ but, as said, I fear it that this is instead correct: $$ \exists x \Big(Mx \land \forall y(My \rightarrow y=x) \land Hx \Big)$$ where Mx stands for 'x is a major of London'.
Any ideas? I can't find anywhere online that says anything about this. The only examples I can find is of the second style, which is why I am worried.