Gödel's Incompleteness Theorems

Theorem

The logician Kurt Friedrich Gödel published two of these:

Gödel's First Incompleteness 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.

$T$ cannot be both consistent and complete.

Gödel's Second Incompleteness Theorem

Gödel's Second Incompleteness Theorem

Sources

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