Hello
A is a formula with variables x and y. What is the difference between
$\displaystyle \forall$ (x,y) A
$\displaystyle \forall $(x)$\displaystyle \forall $(y)A
Thank you...
If $\displaystyle \mathcal{L}$ is a first order language with variable letters $\displaystyle x,y,\ldots$ then, $\displaystyle (\forall x)(\forall y)A$ is a well formed formula and $\displaystyle (\forall (x,y))A$ it is not. We can of course use $\displaystyle (\forall (x,y))A$ as an alternative notation for $\displaystyle (\forall x)(\forall y)A$ .