Theory of Recursive Functions
Gödel's Incompleteness Theorems are two fundamental results in mathematical logic established by Kurt Gödel in the early 20th century. They show that within any consistent formal system capable of expressing basic arithmetic, there are statements that cannot be proven true or false using the rules and axioms of that system. This idea connects deeply to the limitations of computability and the boundaries of what can be resolved within formal systems, which ties into broader concepts such as the Church-Turing thesis and the nature of undecidable problems like the halting problem.
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