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Characterisation of quadratic spaces over the Hilbert field by means of the orthogonality relation

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An orthoset is a set equipped with a symmetric, irreflexive binary relation. With any (anisotropic) Hermitian space H, we may associate the orthoset ( P ( H ) , ⊥ ) , consisting of the set of one-dimensional subspaces of H and the usual orthogonality re... ...