ADMISSIBILITY IN ∑n0-ENUMERATIONS

Abstract

In the paper we introduce the notion of $\sum _n^0\mathit{\text{ partial enumeration}}$ of an abstract structure $\mathfrak{A}$. Given a $k\le n$, we obtain a characterization of the subsets of $\mathfrak{A}$ possessing $\sum _k^0$ pullbacks in all $\sum _n^0$ partial enumerations of $\mathfrak{A}$.