ADMISSIBILITY IN $\sum_n^0$-ENUMERATIONS

Abstract

In the paper we introduce the notion of $\sum_n^0 \textit{ partial enumeration}$ of an abstract structure $\mathfrak{A}$. Given a $k \leq n$, we obtain a characterization of the subsets of $\mathfrak{A}$ possessing $\sum_k^0$ pullbacks in all $\sum_n^0$ partial enumerations of $\mathfrak{A}$.