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== Notation ==
The statement of the theorems refers to an [[admissible numbering]] <math>\varphi</math> of the [[partial recursive function]]s, such that the function corresponding to index <math>e</math> is <math>\varphi_e</math>
If <math>F</math> and <math>G</math> are [[partial function]]s on the natural numbers, the notation <math>F \simeq G</math> indicates that, for each ''n'', either <math>F(n)</math> and <math>G(n)</math> are both defined and are equal, or else <math>F(n)</math> and <math>G(n)</math> are both undefined.
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