Singleton-language problem for Turing machines ($\{⟨M⟩:|L(M)|=1\}$)

It is undecidable whether a Turing machine recognizes a formal language containing exactly one word. Reduce the halting problem by a Turing machine that rejects every nonempty input and, on the empty word, simulates a fixed computation and accepts if that computation halts. Its recognized formal language is a singleton exactly when the fixed computation halts.