Church's Theorem

Theorem

There exists no effective procedure for determining whether or not a given well-formed formula of the predicate calculus is a theorem.

That is, the decision problem for the predicate calculus is undecidable.

Proof

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Source of Name

This entry was named for Alonzo Church.

Historical Note

Church's Theorem was proved by Alonzo Church in $1935$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Church's theorem (A. Church, 1936)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): decidable
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Church's theorem (A. Church, 1936)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): decidable