On Finch's conditions for the completion of orthomodular posets

fazio, davide

;ledda, antonio;paoli, francesco

2023-01-01

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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.