On the Order of a Minimal Additive Basis Original Research Article

LetAbe a set of non-negative integers. If every sufficiently large integer is the sum ofhnot necessarily distinct elements ofA, thenAis called anasymptotic basis of order h. An asymptotic basisAof orderhis called minimal if no proper subset ofAis an asymptotic basis of orderh. It is proved that for every integerhgreater-or-equal, slanted3, no setAis simultaneously a minimal asymptotic basis of ordershand 2h. Forh=2, the problem had already been solved.