A theory is decidable iff there is an algorithm which can determine whether or not any sentence 
is a member of the theory.
Decidable
See also
Church-Turing Thesis, Deterministic, Gödel's Completeness Theorem, Gödel's First Incompleteness Theorem, Gödel's Second Incompleteness Theorem, Kreisel Conjecture, Recursively Undecidable, Rice's Theorem, Richardson's Theorem, Sentence, Tarski's Theorem, Theory, UndecidableExplore with Wolfram|Alpha
References
Enderton, H. B. Elements of Set Theory. New York: Academic Press, 1977.Kemeny, J. G. "Undecidable Problems of Elementary Number Theory." Math. Ann. 135, 160-169, 1958.Referenced on Wolfram|Alpha
DecidableCite this as:
Weisstein, Eric W. "Decidable." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Decidable.html