What is the most common way of naming a large number of variables in predicate logic?
I run out of variables pretty easy in long predicate logic sentences. The simple fact of using a lot of letters as variables are hard enough, but the problem is even bigger when i run out of letters and need to use subscript numbers, as in $x_{5}$, $y_{4}$, and so on.
What is the best way of naming a lot of variables in predicate calculus, without making the sentence unintelligible?
One option is to exclusively use subscripts to distinguish the variables, e.g. $x_1,\,\cdots x_{100}$. In practice you'll probably find some subset of the variables deserve to be thought of in aggregate, so they may share a letter with each other but not other things. For example, if I stated the formula expressing the product of two sums of eight squares as the sum of eight squares, I'd put $\sum_{i=1}^8 a_i^2\sum_{j=1}^8 b_j^2=\sum_{k=1}^8 c_k^2$ followed by explicit formulae for the $c_k$. What I wouldn't do is write $\sum_{i=1}^8 a_i^2\sum_{j=9}^{16} a_j^2=\sum_{k=17}^{24}a_k^2$.