Abstract
An asymptotic basis A of order h is minimal if no proper subset of A is an asymptotic basis of order h. Examples are constructed of minimal asymptotic bases, and also of an asymptotic basis of order two no subset of which is minimal. If B is a set of nonnegative integers which is not a basis (resp. asymptotic basis) of order h, but such that every proper superset of B is a basis (resp. asymptotic basis) of order h, then B is a maximal nonbasis (resp. maximal asymptotic nonbasis) of order h. Examples of such sets are constructed, and it is proved that every set not a basis of order h is a subset of a maximal nonbasis of order h.
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