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Gödel’s Incompleteness Theorems are two theorems among the most fundamental results in modern logic, concerning the limits of provability in formal axiomatic systems. Published in 1931 by Austrian logician and philosopher Kurt Gödel, these theorems have had profound implications in fields such as the foundations of mathematics, formalism, and computability theory. The first incompleteness theorem states that any consistent formal system capable of expressing a certain amount of arithmetic contai