Almost Existentially Closed Models in Positive Logic
This paper explores the concept of almost positively closed models in the framework of positive logic. To accomplish this, we initially define various forms of the positive amalgamation property, such as h-amalgamation and symmetric and asymmetric amalgamation properties. Subsequently, we introduce...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/5595281 |
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| _version_ | 1832559281136730112 |
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| author | Mohammed Belkasmi |
| author_facet | Mohammed Belkasmi |
| author_sort | Mohammed Belkasmi |
| collection | DOAJ |
| description | This paper explores the concept of almost positively closed models in the framework of positive logic. To accomplish this, we initially define various forms of the positive amalgamation property, such as h-amalgamation and symmetric and asymmetric amalgamation properties. Subsequently, we introduce certain structures that enjoy these properties. Following this, we introduce the concepts of Δ-almost positively closed and Δ-weekly almost positively closed. The classes of these structures contain and exhibit properties that closely resemble those of positive existentially closed models. In order to investigate the relationship between positive almost closed and positive strong amalgamation properties, we first introduce the sets of positive algebraic formulas ET and AlgT and the properties of positive strong amalgamation. We then show that if a model A of a theory T is a ET+A-weekly almost positively closed, then A is a positive strong amalgamation basis of T, and if A is a positive strong amalgamation basis of T, then A is AlT+A-weekly almost positively closed. |
| format | Article |
| id | doaj-art-68f875e681514ab1b9bf3a5f9f064064 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-68f875e681514ab1b9bf3a5f9f0640642025-02-03T01:30:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252024-01-01202410.1155/2024/5595281Almost Existentially Closed Models in Positive LogicMohammed Belkasmi0Department of Mathematics College of SciencesThis paper explores the concept of almost positively closed models in the framework of positive logic. To accomplish this, we initially define various forms of the positive amalgamation property, such as h-amalgamation and symmetric and asymmetric amalgamation properties. Subsequently, we introduce certain structures that enjoy these properties. Following this, we introduce the concepts of Δ-almost positively closed and Δ-weekly almost positively closed. The classes of these structures contain and exhibit properties that closely resemble those of positive existentially closed models. In order to investigate the relationship between positive almost closed and positive strong amalgamation properties, we first introduce the sets of positive algebraic formulas ET and AlgT and the properties of positive strong amalgamation. We then show that if a model A of a theory T is a ET+A-weekly almost positively closed, then A is a positive strong amalgamation basis of T, and if A is a positive strong amalgamation basis of T, then A is AlT+A-weekly almost positively closed.http://dx.doi.org/10.1155/2024/5595281 |
| spellingShingle | Mohammed Belkasmi Almost Existentially Closed Models in Positive Logic International Journal of Mathematics and Mathematical Sciences |
| title | Almost Existentially Closed Models in Positive Logic |
| title_full | Almost Existentially Closed Models in Positive Logic |
| title_fullStr | Almost Existentially Closed Models in Positive Logic |
| title_full_unstemmed | Almost Existentially Closed Models in Positive Logic |
| title_short | Almost Existentially Closed Models in Positive Logic |
| title_sort | almost existentially closed models in positive logic |
| url | http://dx.doi.org/10.1155/2024/5595281 |
| work_keys_str_mv | AT mohammedbelkasmi almostexistentiallyclosedmodelsinpositivelogic |