Formalising Definite Description (Russell) 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
l: London

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.
Thanks :)

When you modified the predicate $M$ to mean "$x$ is a mayor of $y$" (in the second gray box), the notation should have become $Mxy$ instead of $Mx$.  Apart from that, your proposed formalization looks fine to me.
