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>The free orthomodular lattice on countably many generators is a subalgebra of the free orthomodular lattice on three generators
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The free orthomodular lattice on countably many generators is a subalgebra of the free orthomodular lattice on three generators
We show every at most countable orthomodular lattice is a subalgebra of one generated by three elements. As a corollary we obtain that the free orthomodular lattice on countably many generators is a subalgebra of the free orthomodular lattice on three generators. This answers a question raised by Bruns in 1976 [2] and listed as Problem 15 in Kalmbach's book on orthomodular lattices [6].
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