On the set-representable orthomodular posets that are point-distinguishing

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the set-representable orthomodular posets that are point-distinguishing

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the set-representable orthomodular posets that are point-distinguishing

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Theoretical Physics

ISSN

0020-7748

e-ISSN

1572-9575

Svazek periodika

62

Číslo periodika v rámci svazku

190

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

6

Strana od-do

—

Kód UT WoS článku

001057776000002

EID výsledku v databázi Scopus

2-s2.0-85168671533