Article
| Title: | Monadic quasi-modal distributive nearlattices (English) |
| Author: | Calomino, Ismael |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 161-174 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We prove that there is a one to one correspondence between monadic finite quasi-modal operators on a distributive nearlattice and quantifiers on the distributive lattice of its finitely generated filters, extending the results given in ``Calomino I., Celani S., González L. J.: Quasi-modal operators on distributive nearlattices, Rev. Unión Mat. Argent. 61 (2020), 339--352". (English) |
| Keyword: | distributive nearlattice |
| Keyword: | modal operator |
| Keyword: | filter |
| MSC: | 03G25 |
| MSC: | 06A12 |
| MSC: | 06D75 |
| idZBL: | Zbl 07790589 |
| idMR: | MR4658997 |
| DOI: | 10.14712/1213-7243.2023.027 |
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| Date available: | 2023-12-13T13:33:41Z |
| Last updated: | 2024-02-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151861 |
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| Reference: | [1] Abbott J. C.: Semi-boolean algebra.Mat. Vesnik 19 (1967), no. 4, 177–198. MR 0239957 |
| Reference: | [2] Araújo J., Kinyon M.: Independent axiom systems for nearlattices.Czech. Math. J. 61(136) (2011), no. 4, 975–992. MR 2886250, 10.1007/s10587-011-0062-6 |
| Reference: | [3] Calomino I., Celani S. A., González L. J.: Quasi-modal operators on distributive nearlattices.Rev. Un. Mat. Argentina 61 (2020), no. 2, 339–352. MR 4198915, 10.33044/revuma.v61n2a10 |
| Reference: | [4] Celani S.: Quasi-modal algebras.Math. Bohem. 126 (2001), no. 4, 721–736. MR 1869464, 10.21136/MB.2001.134115 |
| Reference: | [5] Celani S., Calomino I.: Stone style duality for distributive nearlattices.Algebra Universalis 71 (2014), no. 2, 127–153. MR 3183387, 10.1007/s00012-014-0269-0 |
| Reference: | [6] Celani S., Calomino I.: On homomorphic images and the free distributive lattice extension of a distributive nearlattice.Rep. Math. Logic 51 (2016), 57–73. MR 3562693 |
| Reference: | [7] Celani S., Calomino I.: Distributive nearlattices with a necessity modal operator.Math. Slovaca 69 (2019), no. 1, 35–52. MR 3903625, 10.1515/ms-2017-0201 |
| Reference: | [8] Chajda I., Halaš R.: An example of a congruence distributive variety having no near-unanimity term.Acta Univ. M. Belii Ser. Math. (2006), no. 13, 29–31. MR 2353310 |
| Reference: | [9] Chajda I., Halaš R., Kühr J.: Semilattice Structures.Research and Exposition in Mathematics, 30, Heldermann Verlag, Lemgo, 2007. MR 2326262 |
| Reference: | [10] Chajda I., Kolařík M.: Nearlattices.Discrete Math. 308 (2008), no. 21, 4906–4913. Zbl 1151.06004, MR 2446101 |
| Reference: | [11] Cignoli R.: Quantifiers on distributive lattices.Discrete Math. 96 (1991), no. 3, 183–197. MR 1139446, 10.1016/0012-365X(91)90312-P |
| Reference: | [12] Cornish W. H., Hickman R. C.: Weakly distributive semilattices.Acta Math. Acad. Sci. Hungar. 32 (1978), no. 1–2, 5–16. Zbl 0497.06005, MR 0551490, 10.1007/BF01902195 |
| Reference: | [13] González L. J.: The logic of distributive nearlattices.Soft Comput. 22 (2018), no. 9, 2797–2807. 10.1007/s00500-017-2750-0 |
| Reference: | [14] González L. J.: Selfextensional logics with a distributive nearlattice term.Arch. Math. Logic 58 (2019), no. 1–2, 219–243. MR 3902813, 10.1007/s00153-018-0628-1 |
| Reference: | [15] González L. J., Calomino I.: A completion for distributive nearlattices.Algebra Universalis 80 (2019), no. 4, Paper No. 48, 21 pages. MR 4040591, 10.1007/s00012-019-0622-4 |
| Reference: | [16] González L. J., Calomino I.: Finite distributive nearlattices.Discrete Math. 344 (2021), no. 9, Paper No. 112511, 8 pages. MR 4274211, 10.1016/j.disc.2021.112511 |
| Reference: | [17] Halaš R.: Subdirectly irreducible distributive nearlattices.Miskolc Math. Notes 7 (2006), no. 2, 141–146. Zbl 1120.06003, MR 2310273, 10.18514/MMN.2006.140 |
| Reference: | [18] Halmos P. R.: Algebraic logic. I. Monadic Boolean algebras.Compositio Math. 12 (1956), 217–249. MR 0078304 |
| Reference: | [19] Hickman R.: Join algebras.Comm. Algebra 8 (1980), no. 17, 1653–1685. MR 0585925, 10.1080/00927878008822537 |
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