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{{Orphan|date=July 2008}}
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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* H. Rogers, Jr., 1967. ''The Theory of Recursive Functions and Effective Computability'', second edition 1987, MIT Press. ISBN 0-262-68052-1 (paperback), ISBN 0-07-053522-1.
* {{Citation | last1=Soare | first1=Robert I. | title=Automorphisms of the lattice of recursively enumerable sets. I. Maximal sets | doi=10.2307/1970842 | id={{MathSciNet | id = 0360235}} | year=1974 | journal=[[Annals of Mathematics|Annals of Mathematics. Second Series]] | issn=0003-486X | volume=100 | pages=80–120}}
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