OPEN
If $A_1,A_2$ are disjoint additive bases of order $2$ (i.e. $A_i+A_i$ contains all large integers) then must $A=A_1\cup A_2$ contain a minimal additive basis of order $2$ (one such that deleting any element creates infinitely many $n\not\in A+A$)?
A question of Erdős and Nathanson
[ErNa88].
Härtter [Ha56] and Nathanson [Na74] proved that there exist additive bases which do not contain any minimal additive bases.
