Gödel's Incompleteness Theorems/Second
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Theorem
Let $T$ be the set of theorems of some recursive set of sentences in the language of arithmetic such that $T$ contains minimal arithmetic.
Let $\map {\mathrm {Cons} } T$ be the propositional function which states that $T$ is consistent.
Then it is not possible to prove $\map {\mathrm {Cons} } T$ by means of formal statements within $T$ itself.
Proof
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Also see
Source of Name
This entry was named for Kurt Friedrich Gödel.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: Gödel's proof
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: Gödel's proof
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: Gödel's Incompleteness Theorems