Cardinality of formal languages
The thing you need to remember is that even if Σ has only one symbol , Σ* still has infinite strings over that one symbol , even if Σ = {a} , Σ* = {ε,a,aa,aaa,....} , (a^n , n≥ 0) , Σ* has infinite strings just like with any other alphabet , and so we can form infinite languages over an alphabet with a single symbol just like other alphabet , if now you are convinced that Σ* is infinite even if |Σ|=1  just like any other alphabet , then just as you believe that P(Σ*) for  |Σ| &gt;1 is uncountably infinite , hopefully you can see now that P(Σ*) for |Σ| = 1 is also uncountably infinite , since in both cases it is P(some infinite language) , which in both cases is uncountably infinite