The method of arithmetization, as developed by Gödel [10], exploits the possibility of defining within a formal theory T , or in arithmetical theories closely related to T, various syntactical and logical notions concerning T. In broad terms, the applications of the method can be classified as being extensional if essentially only numerically correct definitions are needed, or in tensional if the definitions must more fully express the notions involved, so that various of the general properties of these notions can be formally derived.
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