For any integer \(h\geqslant 2\), a set of integers \(B=\{b_i\}_{i\in I}\) is a \(B_h\)-set if all h-sums \(b_{i_1}+\ldots +b_{i_h}\) with \(i_1<\ldots <i_h\) are distinct. Answering a question of Alon and Erdős [2], for every \(h\geqslant 2\) we construct a set of integers X which is not a union of finitely many \(B_h\)-sets, yet any finite subset \(Y\subseteq X\) contains an \(B_h\)-set Z with \(|Z|\geqslant \varepsilon |Y|\), where \(\varepsilon :=\varepsilon (h)\). We also discuss questions related to a problem of Pisier about the existence of a set A with similar properties when replacing \(B_h\)-sets by the requirement that all finite sums \(\sum _{j\in J}b_j\) are distinct.

对于任何整数 \(h\geqslant 2\)，如果所有 h 和 \( b_{i_1}+\ldots +b_{i_h}\) 与 \(i_1<\ldots <i_h\) 是不同的。回答 Alon 和 Erdős [2] 的问题，对于每个 \(h\geqslant 2\)，我们构造一组整数 X，它不是有限多个 \(B_h\) 集合的并集，而是任何有限子集 \( Y\subseteq X\) 包含一个 \(B_h\) 集合 Z，其中 \(|Z|\geqslant \varepsilon |Y|\)，其中 \(\varepsilon :=\varepsilon (h)\)。我们还讨论了与 Pisier 问题相关的问题，即当用所有有限和 \(\sum _{j\in J}b_j\) 替换 \(B_h\) 集合时，是否存在具有相似属性的集合 A是不同的。