metalogic: Definition from Answers.com

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The metalogic of a system of logic is the formal theory of the formal logic. Results in metalogic will consist of such things as formal proofs demonstrating the soundness of the logic.

Major results in metalogic include:

The completeness and consistency of first-order logic.
The deduction theorem.
Gödel's completeness theorem.
Gödel's incompleteness theorems.

See proof theory.

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