Erdős Problem 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.
Mathematical statement
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?
Statement source: Erdős Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
erdos_881
theorem erdos_881 : answer(sorry) ↔ ∀ (k : ℕ) (A : Set ℕ), IsMinimalAsymptoticAddBasisOfOrder k A → ∃ (B : Set ℕ), B ⊆ A ∧ B.Infinite ∧ (A \ B).IsAsymptoticAddBasisOfOrder (k + 1) := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References