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Revision as of 15:29, 14 June 2007

An orthomodular lattice is an orthocomplemented lattice L {\displaystyle L} that satisfies the following condition for all x , y ∈ L {\displaystyle x,y\in L} :

If x ≤ y {\displaystyle x\leq y} then y = x ∨ ( x ⊥ ∧ y ) {\displaystyle y=x\lor (x^{\perp }\land y)}

Lattices of this form are of crucial importance for the study of quantum logic, since they are part of the axiomisation of the Hilbert space formulation of quantum mechanics.

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