On the conservativity of the axiom of choice over set theory

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

Abstract
We show that for various set theories T including ZF, T + AC is conservative over T for sentences of the form ${\forall x \exists ! y}$ A(x, y) where A(x, y) is a Δ0 formula
Keywords Axiom of choice  Conservativity  Forcing
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DOI 10.1007/s00153-011-0248-5
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Admissible Sets and Structures.Jon Barwise - 1978 - Studia Logica 37 (3):297-299.

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