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DOE OSTI · 21501255

Atomic effect algebras with compression bases

Caragheorgheopol, Dan·Tkadlec, Josef
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Abstract

Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS97 MATHEMATICS AND COMPUTINGALGEBRAATOMSCOMPRESSIONMATHEMATICAL LOGICMATHEMATICSMECHANICSQUANTUM MECHANICS

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Caragheorgheopol, Dan, Tkadlec, Josef. 2011-01-15. Atomic effect algebras with compression bases. https://doi.org/10.1063/1.3533918

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