An equation calculus for primitive recursive rational-valued functions

An equation calculus $\mathbb M$ primitive recursive functions of the positive rational argument is constructed in this paper. Among the axioms and inference roles of $\mathbb M$ there are the postulates of the primitive recursive arithmetic (ERA) by Goodstein. Logical constants $\&,\vee,\rceil,\to,\leftrightarrow,\forall_{\leq},\exists_{\leq}$ can be defined in $\mathbb M$. It is proved that $\mathbb M$ is a conservative extension of PRA.