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Erschienen in:
26.11.2019 | Foundations
Spectral resolutions and observables in n-perfect MV-algebras
Erschienen in: Soft Computing | Ausgabe 2/2020
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Abstract
We define an observable as a kind of a \(\sigma \)-homomorphism from the Borel \(\sigma \)-algebra of the real line into a \(\mathrm{Rad}\)-Dedekind \(\sigma \)-complete n-perfect MV-algebra with principal radical preserving disjoint unions. We show that there is a one-to-one correspondence between spectral resolutions (defined now with four properties and not with three ones). This correspondence allows us to define a partial order on the set of observables, called the Olson order, as well as a sum of observables which converts the set of observables into a commutative lattice-ordered semigroup with respect to the Olson order and with the sum of observables.