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Erdős problem 701

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Let F\mathcal{F} be a family of sets closed under taking subsets (i.e. if B⊆A∈FB\subseteq A\in\mathcal{F} then B∈FB\in \mathcal{F}). There exists some element xx such that whenever F′⊆F\mathcal{F}'\subseteq \mathcal{F} is an intersecting subfamily we have ∣F′∣≤∣{A∈F:x∈A}∣.\lvert \mathcal{F}'\rvert \leq \lvert \{ A\in \mathcal{F} : x\in A\}\rvert.

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  2. StatementRetained
  3. Formal1 retained
  4. ResolutionNone filed
  5. WorkNone recorded
  6. DecisionNone here
  7. The questionNot reached
What this record is missingResolution

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Combinatorics47Intersecting Family5
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