Additive systems for $\mathbb{Z}$ are undecidable

Andrei Zabolotskii

What are the collections of sets $A_i\subset \mathbb{Z}$ such that any $n\in \mathbb{Z}$ has exactly one representation as $n=a_0+a_1+\cdots$ with $a_i\in A_i$? The answer for $\m…