Mathematics
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History of mathematics
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Uncertainty principle
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Epistemology
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Foundations of mathematics
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Mathematical logic
Metatheorem
Kurt Gödel
Theorem
Model theory
Mathematical theorem
Proof theory
Undecidable problem
Hilbert's second problem
Orch-OR
Theorems in the foundations of mathematics
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
Metatheorems
Hilbert's program
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, pro...
Proof sketch for Gödel's first incompleteness theorem
Proof sketch for Gödel's first incompleteness theorem
This article gives a sketch of a proof of Gödel's first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses, which are discussed as needed dur...