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'Undecidable' has more than one meaning:
In mathematical logic:
★ A decision problem is called (recursively) undecidable if no algorithm can decide it, such as for Turing's halting problem; see also under Decidable.
★ "Undecidable" is sometimes used as a synonym of "independent", where a formula in mathematical logic is independent of a logical theory if neither that formula nor its negation can be proved within the theory.
In mathematical logic:
★ A decision problem is called (recursively) undecidable if no algorithm can decide it, such as for Turing's halting problem; see also under Decidable.
★ "Undecidable" is sometimes used as a synonym of "independent", where a formula in mathematical logic is independent of a logical theory if neither that formula nor its negation can be proved within the theory.
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