Erdős #881 (?, AMS 5 11). STATEMENT: We interpret "additive basis of order `k`" as an asymptotic additive basis of order `k`, using the predicate `Set.IsAsymptoticAddBasisOfOrder` from additive combinatorics. A *minimal* additive basis of order `k` is a set `A` such that * `A` is an asymptotic additive basis of order `k`, and * for every infinite subset `B ⊆ A`, the complement `A \ B` is *not* an asymptotic additive basis of order `k`. FORMAL: erdos_881: answer(sorry) ↔ ∀ (k : ℕ) (A : Set ℕ), IsMinimalAsymptoticAddBasisOfOrder k A → ∃ (B : Set ℕ), B ⊆ A ∧ B.Infinite ∧ (A \ B).IsAsymptoticAddBasisOfOrder (k + 1) KNOWN/REMARKS: # Erdős Problem 881 *Reference:* erdosproblems.com/881 | Let `A ⊂ ℕ` be an additive basis of order `k` which is minimal in the sense that if `B ⊂ A` is any infinite set, then `A \ B` is not a basis of order `k`. Must there exist an infinite `B ⊂ A` such that `A \ B` is an additive basis of order `k + 1`? RELATED: [] OEIS: []

id

vpr_a81e260d7a01be47

frontier

Erdős problems frontier

kind

finding.add

created

2026-06-04