On the set-representable orthomodular posets that are point-distinguishing
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00367665" target="_blank" >RIV/68407700:21230/23:00367665 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10773-023-05436-3" target="_blank" >https://doi.org/10.1007/s10773-023-05436-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-023-05436-3" target="_blank" >10.1007/s10773-023-05436-3</a>
Alternative languages
Result language
angličtina
Original language name
On the set-representable orthomodular posets that are point-distinguishing
Original language description
Let us denote by SOMP the class of all set-representable orthomodular posets and by PDSOMP those elements of SOMP in which any pair of points in the underlying set P can be distinguished by a set (i.e., (P,L) element PDSOMP precisely when for any pair x,y element P there is a set A element L with x element A and y element/ A). In this note we first construct, for each (P, L) element SOMP, a point-distinguishing orthomodular poset that is isomorphic to (P,L). We show that by using a generalized form of the Stone representation technique we also obtain point-distinguishing representations of ( P , L). We then prove that this technique gives us point-distinguishing representations on which all two-valued states are determined by points (all two-valued states are Dirac states). Since orthomodular posets may be regarded as abstract counterparts of event structures about quantum experiments, results of this work may have some relevance for the foundation of quantum mechanics.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Theoretical Physics
ISSN
0020-7748
e-ISSN
1572-9575
Volume of the periodical
62
Issue of the periodical within the volume
190
Country of publishing house
US - UNITED STATES
Number of pages
6
Pages from-to
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UT code for WoS article
001057776000002
EID of the result in the Scopus database
2-s2.0-85168671533