In this paper, we aim at highlighting the significance of the Aand B- properties introduced by P.D. Finch in [16]. These conditions turn out to capture interesting structural features of lattices of closed subspaces of complete inner vector spaces. Moreover, we generalise them to the context of effect algebras, establishing a novel connection between quantum structures (orthomodular posets, orthoalgebras, effect algebras) arising from the logicoalgebraic approach to quantum mechanics.
On Finch's conditions for the completion of orthomodular posets
fazio, davide
;ledda, antonio;paoli, francesco
2023-01-01
Abstract
In this paper, we aim at highlighting the significance of the Aand B- properties introduced by P.D. Finch in [16]. These conditions turn out to capture interesting structural features of lattices of closed subspaces of complete inner vector spaces. Moreover, we generalise them to the context of effect algebras, establishing a novel connection between quantum structures (orthomodular posets, orthoalgebras, effect algebras) arising from the logicoalgebraic approach to quantum mechanics.
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