Unary counting quantifiers do not increase the expressive power of Presburger aritmetic: an alternative shorter proof

This work was presented in June 5-7, 2017 at the conference “Journées sur les Arithmétiques Faibles – Weak Arithmetics Days” held in Saint-Pertersburg of which no proceeding was ever published. It was not a new result but showed that a different approach is possible. The paper presented at ICALP 2024 addresses, among other problems, the complexity issues which were ignored in my 2017 talk.