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In [[recursion theory]], the [[mathematics|mathematical]] theory of computability, a '''maximal set''' is a coinfinite [[recursively enumerable set|recursively enumerable subset]] ''A'' of the [[natural number]]s such that for every further recursively enumerable subset ''B'' of the natural numbers, either ''B'' is [[cofinite]] or ''B'' is a finite variant of ''A'' or ''B'' is not a superset of ''A''. This gives an easy definition within the [[lattice (order)|lattice]] of the recursively enumerable sets.
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