On the universal theory of the free pseudocomplemented distributive lattice
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912480074137600 |
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| author | Carai, Luca Moraschini, Tommaso |
| author_facet | Carai, Luca Moraschini, Tommaso |
| contents | It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free algebras which is known to be undecidable. As a by-product, a description of the finitely generated pseudocomplemented distributive lattices that can be embedded into the free algebra is also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the universal theory of the free pseudocomplemented distributive lattice Carai, Luca Moraschini, Tommaso Logic It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free algebras which is known to be undecidable. As a by-product, a description of the finitely generated pseudocomplemented distributive lattices that can be embedded into the free algebra is also obtained. |
| title | On the universal theory of the free pseudocomplemented distributive lattice |
| topic | Logic |
| url | https://arxiv.org/abs/2409.03640 |