Gödel's Incompleteness Theorems/Second

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

• Gödel's First Incompleteness Theorem

Source of Name

This entry was named for Kurt Friedrich Gödel.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Gödel's proof
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Gödel's proof
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Gödel's Incompleteness Theorems