## Unavoidable subprojections in union-closed set systems of infinite breadth.(English)Zbl 07333298

Summary: We consider union-closed set systems with infinite breadth, focusing on three particular configurations $$\mathcal{T}_{\max}(\mathcal{E})$$, $$\mathcal{T}_{\min}(\mathcal{E})$$ and $$\mathcal{T}_{\operatorname{ort}}(\mathcal{E})$$. We show that these three configurations are not isolated examples; in any given union-closed set system of infinite breadth, at least one of these three configurations will occur as a subprojection. This characterizes those union-closed set systems which have infinite breadth, and is the first general structural result for such set systems.

### MSC:

 20Axx Foundations 03Cxx Model theory 03Gxx Algebraic logic
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### References:

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