Bochvar algebras: A categorical equivalence and the generated variety
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916532801503232 |
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| author | Bonzio, Stefano Paoli, Francesco Baldi, Michele Pra |
| author_facet | Bonzio, Stefano Paoli, Francesco Baldi, Michele Pra |
| contents | The proper quasivariety BCA of Bochvar algebras, which serves as the equivalent algebraic semantics of Bochvar's external logic, was introduced by Finn and Grigolia in and extensively studied in a recent work by two of these authors. In this paper, we show that the algebraic category of Bochvar algebras is equivalent to a category whose objects are pairs consisting of a Boolean algebra and a meet-subsemilattice (with unit) of the same. Furthermore, we provide an axiomatisation of the variety $V(BCA) generated by Bochvar algebras. Finally, we axiomatise the join of Boolean algebras and semilattices within the lattice of subvarieties of V(BCA). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bochvar algebras: A categorical equivalence and the generated variety Bonzio, Stefano Paoli, Francesco Baldi, Michele Pra Logic Commutative Algebra Category Theory 03G25, 03B60 The proper quasivariety BCA of Bochvar algebras, which serves as the equivalent algebraic semantics of Bochvar's external logic, was introduced by Finn and Grigolia in and extensively studied in a recent work by two of these authors. In this paper, we show that the algebraic category of Bochvar algebras is equivalent to a category whose objects are pairs consisting of a Boolean algebra and a meet-subsemilattice (with unit) of the same. Furthermore, we provide an axiomatisation of the variety $V(BCA) generated by Bochvar algebras. Finally, we axiomatise the join of Boolean algebras and semilattices within the lattice of subvarieties of V(BCA). |
| title | Bochvar algebras: A categorical equivalence and the generated variety |
| topic | Logic Commutative Algebra Category Theory 03G25, 03B60 |
| url | https://arxiv.org/abs/2412.14911 |