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Let $K$ be a field of cardinality $\kappa$. Fix a bijection between $\kappa$ and the projective plane over $K$. Then let $F$ be (the image under this bijection of) the set of lines in the projective plane.
Let $K$ be a field of cardinality $\kappa$. Fix a bijection between $\kappa$ and the projective plane over $K$. Then let $F$ be (the image under this bijection) the set of lines in the projective plane.
Let $K$ be a field of cardinality $\kappa$. Fix a bijection between $\kappa$ and the projective plane over $K$. Then let $F$ be (the image under this bijection of) the set of lines in the projective plane.
Let $K$ be a field of cardinality $\kappa$. Fix a bijection between $\kappa$ and the projective plane over $K$. Then let $F$ be (the image under this bijection) the set of lines in the projective plane.
