Problem 1173

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Statement. Assume the generalised continuum hypothesis. Let

$$f: \omega_{\omega+1}\to [\omega_{\omega+1}]^{\leq \aleph_\omega}$$

be a set mapping such that

$$\lvert f(\alpha)\cap f(\beta)\rvert <\aleph_\omega$$

for all $\alpha\neq \beta$. Does there exist a free set of cardinality $\aleph_{\omega+1}$?

Status. Open. The site's label is OPEN.

Source. erdosproblems.com/1173, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #1173, https://www.erdosproblems.com/1173.

Formalization. None recorded.

Current assessment

No current assessment is recorded. The status above is imported from the dated site record. This page records no current literature search or independent assessment of proof coverage.

Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

• kunen_2013_impact_paul_erdos_set_theory
• kunen_2013_impact_paul_erdos_set_theory / theorem_p359_free_set_lemma
• erdos_1974_unsolved_solved_problems_set_theory
• erdos_1974_unsolved_solved_problems_set_theory / problem_35
• erdos_1974_unsolved_solved_problems_set_theory / theorem_p278_shelah
• komjath_2025_erdos_hajnal_problem_list