States On Orthocomplemented Difference Posets (Extensions)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00300847" target="_blank" >RIV/68407700:21230/16:00300847 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11005-016-0862-6" target="_blank" >http://dx.doi.org/10.1007/s11005-016-0862-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11005-016-0862-6" target="_blank" >10.1007/s11005-016-0862-6</a>

Result language
angličtina
Original language name
States On Orthocomplemented Difference Posets (Extensions)
Original language description
We continue the investigation of orthocomplemented posets that are endowed with a symmetric difference (ODPs). The ODPs are orthomodular and, therefore, can be viewed as "enriched" quantum logics. In this note, we introduced states on ODPs. We derive their basic properties and study the possibility of extending them over larger ODPs. We show that there are extensions of states from Boolean algebras over unital ODPs. Since unital ODPs do not, in general, have to be set-representable, this result can be applied to a rather large class of ODPs. We then ask the same question after replacing Boolean algebras with "nearly Boolean" ODPs (the pseudocomplemented ODPs). Making use of a few results on ODPs, some known and some new, we construct a pseudocomplemented ODP, P, and a state on P that does not allow for extensions over larger ODPs.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)