Sheffer operations in complemented posets
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2021
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Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
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Abstract
We show that in every downward directed poset with an antitone involu-tion the so-called Sheffer operation can be introduced satisfying certain identities.However, also conversely, if we have given a Sheffer operation|on a setP, thenPcan be converted into a poset with an antitone involution′, where both′and theorder relation≤are derived by|. Using this, we can characterize orthoposets, i.e.bounded posets with complementation which is an antitone involution by means ofidentities satisfied by this Sheffer operation. Also conversely, if|is a Sheffer oper-ation on a given setPsatisfying these identities, thenPcan be organized into anorthoposet.
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Mathematics for Applications. 2021 vol. 10, č. 1, s. 1-7. ISSN 1805-3629
http://ma.fme.vutbr.cz/archiv/10_1/ma_10_1_chajda_kolarik_final.pdf
http://ma.fme.vutbr.cz/archiv/10_1/ma_10_1_chajda_kolarik_final.pdf
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en
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© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky