A set or language is decidable if its characteristic function is can be computed by an effective method. Use this tag when your question involves the (un-)decidability of a set or language.
A set $S \subseteq \mathbb{N}$ is decidable if its characteristic function $\chi_S$ can be computed by an effective method. Assuming the Church-Turing thesis, this means that $S$ is decidable if $\chi_S$ can be computed by a Turing machine or an equivalent model such as general recursive functions or the $\lambda$-calculus.
A set of arbitrary objects $S$ is decidable if there is an encoding $\langle \cdot \rangle$ s.t. $\{\langle x \rangle : x \in S\}$ is decidable. Some introductions define decidability for formal languages instead of sets of naturals numbers.
Important concepts in decidability include
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