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We establish upper bounds on the number of real multiquadratic fields thatadmit a universal quadratic lattice of a given rank, or contain a given amountof indecomposable elements modulo totally positive units, obtaining densityzero statements. We also study the structure of indecomposable elements in realbiquadratic fields, and compute a system of indecomposable elements modulototally positive units for some families of real biquadratic fields.

Minimal rank of universal lattices and number of indecomposable elements in real multiquadratic fields