Profinite bi-Heyting algebras
| Authors | |
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| Publication date | 08-2025 |
| Journal | Algebra Universalis |
| Article number | 16 |
| Volume | Issue number | 86 | 3 |
| Number of pages | 20 |
| Organisations |
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| Abstract | A poset X is said to be zigzag image-finite, if the least updownset (i.e., both an upset and a downset) containing x is finite, for all x ∈ X. We show that a bi-Heyting algebra is profinite if and only if it is isomorphic to the lattice of upsets of a zigzag image-finite poset. Zigzag image-finite posets have the property of being disjoint unions of finite connected posets. Because of this, we equivalently show that a bi-Heyting algebra is profinite if and only if it is isomorphic to a direct product of simple finite bi-Heyting algebras. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1007/s00012-025-00892-w |
| Other links | https://www.scopus.com/pages/publications/105004667092 |
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Profinite bi-Heyting algebras
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