Об интерпретациях арифметики Пресбургера в арифметиках Бюхи
Büchi arithmetics BAn, , are extensions of Presburger arithmetic with an unary functional symbol
denoting the largest power of n that divides x. Definability of a set in BAn is equivalent to its recognizability
by a finite automaton receiving numbers in their n-ary expansion. We consider the interpretations of Presburger
Arithmetic in the standard model of BAn and show that each such interpretation has an internal model
isomorphic to the standard one. This answers a question by A. Visser on the interpretations of certain weak
arithmetical theories in themselves.