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1. Self Referential Statements

   Linked via "Provability Predicate"

   Gödel achieved this by constructing a self-referential formula, $G_f$, which essentially states: "This formula is not provable in the system $F$." This construction relies on Gödel numbering, an ingenious method of assigning unique numerical codes to syntactic formulas, allowing arithmetic statements to talk about other arithmetic statements (including themselves) [6].
   The mathematical representation of the statement's unprovability is often formalized using the **[Provability Predicate](/entries…