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Statement

Notation (p. 5-01). $\mathbb N_0$ is the set of non-negative integers; for $A\subseteq\mathbb N_0$, $\mathcal D(A)$ is its ordinary-difference set and $\mathcal D_0(A)$ its density-difference set, the $d\in\mathbb N_0$ with $\overline d(A\cap(A-d))>0$; $\overline d$ and $\underline d$ are upper and lower density (the print writes $d^-$ and $d_-$), as on Theorem 2.

Theorem 3 (p. 5-03), with a pointer to Stewart and Tijdeman. Given a set $A\subseteq\mathbb N_0$, there is a set $B\subseteq\mathbb N_0$ with $\underline d(B)\ge\overline d(A)$ such that $\mathcal D(B)\subseteq\mathcal D_0(A)$.

The survey presents it as a tool for translating results about one type of difference set into results about another; it uses it on p. 5-05 in an alternative proof of Theorem 7 and on p. 5-08 to replace $\mathcal D(A)$ by $\mathcal D_0(A)$ in Theorem 8.

Proof pointer

The survey gives no proof; it points to Stewart and Tijdeman, On density-difference sets of sequences of integers (reference [15] of the survey, then to appear).

Read depth

Claims checked: Theorem 3 was read clause by clause on the page image of the print. The proof is not in the survey and was not checked.

Dependencies

None in the corpus. External input: the cited Stewart-Tijdeman paper.

Source. Cam L. Stewart, On difference sets of sets of integers, Séminaire Delange-Pisot-Poitou, Théorie des nombres, 19e année (1977/78), Fasc. 1, Exp. No. 5, 8 pp.; pages are cited by the print's own numbering 5-01 to 5-08, as on the source card.

Bears on

No Erdős problem page of the corpus cites this theorem.