Orthogonality spaces associated with posets
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916487274430464 |
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| author | Jenča, Gejza |
| author_facet | Jenča, Gejza |
| contents | An orthogonality space is a set equipped with a symmetric, irreflexive relation called orthogonality. Every orthogonality space has an associated complete ortholattice, called the logic of the orthogonality space. To every poset, we associate an orthogonality space consisting of proper quotients (that means, nonsingleton closed intervals), equipped with a certain orthogonality relation. We prove that a finite bounded poset is a lattice if and only if the logic of its orthogonality space is an orthomodular lattice. We prove that that a poset is a chain if and only if the logic of the associated orthogonality space is a Boolean algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_08113 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Orthogonality spaces associated with posets Jenča, Gejza Rings and Algebras 2020: 06A06, 06C15 An orthogonality space is a set equipped with a symmetric, irreflexive relation called orthogonality. Every orthogonality space has an associated complete ortholattice, called the logic of the orthogonality space. To every poset, we associate an orthogonality space consisting of proper quotients (that means, nonsingleton closed intervals), equipped with a certain orthogonality relation. We prove that a finite bounded poset is a lattice if and only if the logic of its orthogonality space is an orthomodular lattice. We prove that that a poset is a chain if and only if the logic of the associated orthogonality space is a Boolean algebra. |
| title | Orthogonality spaces associated with posets |
| topic | Rings and Algebras 2020: 06A06, 06C15 |
| url | https://arxiv.org/abs/2206.08113 |