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An $m$-orthocomplete orthomodular lattice is $m$-complete

1970
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Proceedings of the American Mathematical Society
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We call an orthomodular lattice £ m-orthocomplete for an infinite cardinal m if every orthogonal family of Sm elements from £ has a join in £, and we call £ m-complete if every family, orthogonal or not, of %m elements from £ has a join in £. We prove that an »z-orthocomplete orthomodular lattice is mcomplete. Since a Boolean algebra is a distributive orthomodular lattice, we obtain as a special case the Smith-Tarski theorem: An m-orthocomplete Boolean algebra is m-complete. © On-i -JA p + K 8)

doi:10.1090/s0002-9939-1970-0256949-7
fatcat:gi5amomzjbcx3arapw6d6f2kfu