Decidable

A ``theory'' in Logic is decidable if there is an Algorithm that will decide on input $\phi$ whether or not $\phi$ is a Sentence true of the Field of Real Numbers $\Bbb{R}$.

See also Church's Thesis, Gödel's Completeness Theorem, Gödel's Incompleteness Theorem, Kreisel Conjecture, Tarski's Theorem, Undecidable, Universal Statement

References

Kemeny, J. G. ``Undecidable Problems of Elementary Number Theory.'' Math. Ann. 135, 160-169, 1958.