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A [[pointclass]] <math>\boldsymbol{\Gamma}</math> is said to have the '''uniformization property''' if every relation <math>R</math> in <math>\boldsymbol{\Gamma}</math> can be uniformized by a partial function in <math>\boldsymbol{\Gamma}</math>. The uniformization property is implied by the [[scale property]], at least for [[adequate pointclass]]es.
It follows from [[ZFC]] alone that <math>\boldsymbol{\Pi}^1_1</math> and <math>\boldsymbol{\Sigma}^1_2</math> have the uniformization property. It follows from the existence of sufficient [[large cardinal]]s that
*<math>\boldsymbol{\Pi}^1_{2n+1}</math> and <math>\boldsymbol{\Sigma}^1_{2n+2}</math> have the uniformization property for every [[natural number]] <math>n</math>.
*Therefore, the collection of [[projective set]]s has the uniformization property
*Every relation in [[L(R)]] can be uniformized, but ''not necessarily'' by a function in L(R). In fact, L(R) does not have the uniformization property (equivalently, L(R) does not satisfy the axiom of uniformization).
== References ==
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