undecidability of the structure $(\omega,+,2^n)$

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Is the structure $(\omega,+,2^n)$ undecidable? There is no easy way to define multiplication using a formula.

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The same question was asked, by the same user, on MathOverflow, and an answer was accepted there: https://mathoverflow.net/questions/126318/is-the-structure-omega-2n-undecidable .