Sheffer operations in complemented posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609259" target="_blank" >RIV/61989592:15310/21:73609259 - isvavai.cz</a>
Result on the web
<a href="http://ma.fme.vutbr.cz/archiv/10_1/ma_10_1_chajda_kolarik_final.pdf" target="_blank" >http://ma.fme.vutbr.cz/archiv/10_1/ma_10_1_chajda_kolarik_final.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.13164/ma.2021.01" target="_blank" >10.13164/ma.2021.01</a>

Result language
angličtina
Original language name
Sheffer operations in complemented posets
Original language description
We show that in every downward directed poset with an antitone involution can be introduced the so-called Sheffer operation satisfying certain identities. However, also conversely, if we have given a Sheffer operation | on a set P then P can be converted into a poset with an antitone involution ' where both ' and the order relation are derived by |. Using this, we can characterize orthoposets, i.e. bounded posets with complementation which is an antitone involution by means of identities satisfying by this Sheffer operation. Also conversely, if | is a Sheffer operation on a given set P satisfying these identities then P can be organized into an orthoposet.
Czech name
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Czech description
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Project
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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