On the conservativity of the axiom of choice over set theory

Archive for Mathematical Logic 50 (7-8):777-790 (2011)
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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.

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Admissible Sets and Structures.Jon Barwise - 1978 - Studia Logica 37 (3):297-299.
Definability and Computability.Yuri L. Ershov - 1998 - Studia Logica 61 (3):439-441.

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