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Reports on Mathematical Logic

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No. 36

Saeed SALEHI:

**Decidable formulas of Intuitionistic Primitive Recursive Arithmetic**

A b s t r a c t. By formalizing some classical facts about provably total functions
of intuitionistic primitive recursive arithmetic ($iPRA$), we prove that
the set of decidable formulas of $iPRA$ and of $i\Sigma_1^+$ (intuitionistic
$\Sigma_1$-induction in the language of $PRA$) coincides with the set of
its provably $\Delta_1$-formulas and coincides with the set of its provably atomic
formulas.

By the same methods, we shall give another proof of a theorem of Markovi\'{c}
and \mbox{ De Jongh}: the decidable formulas of $HA$ are its provably
$\Delta_1$-formulas.

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