Abstract

We show that for various set theories T including ZF, T + AC is conservative over T for sentences of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall x \exists! y}$$\end{document}A(x, y) where A(x, y) is a Δ0 formula.