States on systems of sets that are closed under symmetric difference

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F15%3A00234486" target="_blank" >RIV/68407700:21230/15:00234486 - isvavai.cz</a>
Result on the web
<a href="http://onlinelibrary.wiley.com/doi/10.1002/mana.201500029/abstract" target="_blank" >http://onlinelibrary.wiley.com/doi/10.1002/mana.201500029/abstract</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.201500029" target="_blank" >10.1002/mana.201500029</a>

Result language
angličtina
Original language name
States on systems of sets that are closed under symmetric difference
Original language description
We consider extensions of certain states. The states are defined on the systems of sets that are closed under the formation of the symmetric difference (concrete quantum logics). These systems can be viewed as certain set-representable quantum logics enriched with the symmetric difference. We first show how the compactness argument allows us to extend states on Boolean algebras over such systems of sets. We then observe that the extensions are sometimes possible even for non-Boolean situations. On the other hand, a difference-closed system can be constructed such that even two-valued states do not allow for extensions.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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