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Let $L$ be the first-order language with binary function symbol $+$, unary function symbol $E$. Let $T$ be the set of sentences over this language that are true in the natural numbers, with $+$ interpreted in the usual way, and $E(n$) interpreted as $2^n$. Is the set $T$ recursive?

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Also asked here: math.stackexchange.com/questions/349383/… – Andrés E. Caicedo Apr 2 '13 at 22:04
    
    
Thank you for the help! – danulg Apr 3 '13 at 11:32
    
Does anybody know a book / other resources about omega structures? – Martin Thoma Feb 26 '15 at 10:32
up vote 4 down vote accepted

As Marty explained in this answer, this question is the central topic of the paper On the expansion $\langle \mathbb{N},+,2^x\rangle$ of Presburger arithmetic, by Françoise Point, based on a joint proceedings paper with G. Cherlin on a result credited to Alexei L. Semenov.

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