We study the \documentclass[12pt]{minimal}
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\begin{document}$ p $\end{document}-reducibility of numberings which was introduced and first studied
by Degtev. \documentclass[12pt]{minimal}
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\begin{document}$ p $\end{document}-Reducibility is an effectively bounded version of the \documentclass[12pt]{minimal}
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\begin{document}$ e $\end{document}-reducibility
of numberings. Also, we prove that for every set \documentclass[12pt]{minimal}
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\begin{document}$ A $\end{document} there exists an \documentclass[12pt]{minimal}
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\begin{document}$ A $\end{document}-computable family
without universal numberings but admitting \documentclass[12pt]{minimal}
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\begin{document}$ p $\end{document}-universal numberings and obtain
a criterion for the existence of \documentclass[12pt]{minimal}
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\begin{document}$ p $\end{document}-universal numberings of finite families of \documentclass[12pt]{minimal}
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\begin{document}$ A $\end{document}-c.e. sets.
Finally, we show that every \documentclass[12pt]{minimal}
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\begin{document}$ A $\end{document}-computable family,
with \documentclass[12pt]{minimal}
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\begin{document}$ \varnothing^{\prime\prime}\leq_{T}A $\end{document}, has infinitely many pairwise non-\documentclass[12pt]{minimal}
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\begin{document}$ p $\end{document}-equivalent
\documentclass[12pt]{minimal}
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\begin{document}$ p $\end{document}-minimal \documentclass[12pt]{minimal}
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\begin{document}$ A $\end{document}-computable numberings.
