Retrieving "Gödel Sentence" from the archives

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1. Kurt Gödel

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   The Second Incompleteness Theorem extends the first, stating that a consistent system $F$ cannot prove its own consistency. Specifically, the statement asserting the consistency of $F$, denoted $\text{Con}(F)$, is itself unprovable within $F$, provided $F$ is consistent. This effectively shattered Hilbert's ambition to secure all of mathematics on a finite, self-justifying foundation.
   The formal assertion of consistency is represented by a complex arithmetic formula, often related to the negatio…