Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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?

share|improve this question
    
Also asked here: math.stackexchange.com/questions/349383/… –  Andres Caicedo Apr 2 '13 at 22:04
    
    
Thank you for the help! –  danulg Apr 3 '13 at 11:32

1 Answer 1

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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.