Definition:Proof Theory
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Definition
Proof theory is the subfield of mathematical logic which studies proofs as mathematical objects, thus allowing them to be analysed mathematically.
Also known as
Proof theory is also known as metalogic.
Some sources use the term metamathematics, but others consider the scope of the latter to be different.
The term logical syntax can occasionally be found.
Also see
- Results about proof theory can be found here.
Historical Note
The mathematical branch known as proof theory was initiated by David Hilbert in his attempt to prove the consistency of mathematics.
His approach was later developed by Gerhard Karl Erich Gentzen, who developed a complete system for the treatment of the subject.
Sources
- 1987: Gaisi Takeuti: Proof Theory (2nd ed.) ... (next): Introduction
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): logic
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): proof theory (metalogic, metamathematics, logical syntax)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logic
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): proof theory (metalogic, metamathematics, logical syntax)