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According to the paper Fragments of Peano's Arithmetic and the MRDP theorem (Section 6), elementary function arithmetic (EFA) is finitely axiomatizable.

Is there a known explicite finite axiomatization? If not, what is an upper bound on the number of axioms needed?

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    $\begingroup$ It's possible to combine multiple axioms into 1 axiom using conjunctions. $\endgroup$
    – Lucenaposition
    Commented Jun 26 at 7:59
  • $\begingroup$ @Lucenaposition I'd say it's more of a trick, but fair enough. What about the first part of my question? $\endgroup$
    – user1343124
    Commented Jun 26 at 8:14
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    $\begingroup$ +1: Good question.@Lucenaposition: it is not possible in general to combine an infinite collection of axioms like the axioms schema of induction in EFA into a single axiom. $\endgroup$
    – Rob Arthan
    Commented Jun 26 at 21:21

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