3 problems

A sequence of positive integers is a Sidon sequence if all sums $a+a'$ with $a,a'$ in the sequence and $a\leq a'$ are distinct; it is an asymptotic basis of order $g$ if every suff…

Let $h\geqslant 2$ and let $f$ be a function for which the notion of a $\Theta(f)$-regular asymptotic $h$-basis is defined. Adapted Erdős 1956 conjecture. There are no $\Theta(f)$-…

Let $h\geqslant 2$, let $\mathcal{S}$ be the space of subsets of the nonnegative integers, and for an asymptotic $h$-basis $A$ let $r_h(n;A)$ denote its representation function. Er…