Abstract

We show that every nonzero Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^{0}_{2}}$$\end{document} enumeration degree bounds the enumeration degree of a 1-generic set. We also point out that the enumeration degrees of 1-generic sets, below the first jump, are not downwards closed, thus answering a question of Cooper.