On the conservativity of the axiom of choice over set theory


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.

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Correspondence to Timothy J. Carlson.

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Carlson, T.J. On the conservativity of the axiom of choice over set theory. Arch. Math. Logic 50, 777 (2011) doi:10.1007/s00153-011-0248-5

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  • Axiom of choice
  • Conservativity
  • Forcing

Mathematics Subject Classification (2000)

  • 03E25