Source labels openChecked July 26, 2026

Erdős Problem 598

Erdős Problem 598:* Let $m$ be an infinite cardinal and $\kappa$ be the successor cardinal of $2^{\aleph_0}$ . Can one colour the countable subsets of $m$ using $\kappa$ many colours so that every $X \subseteq m$ with $|X| = \kappa$ contains subsets of all...

Mathematical logic AMS 3 AMS 5

Mathematical statement

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_598

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_598 : answer(sorry) ↔    ∃ c : { s : Set m // s.Countable } → κ.out,    ∀ X : Set m, #X = κ →    c '' { s : { sub : Set m // sub.Countable } | s.1 ⊆ X } = Set.univ := 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

Pinned Formal Conjectures sourceformalization erdosproblems.com/598background