Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with Δ
Pavelka-style (rational) Gödel logic is an extension of Gödel logic which is denoted by RGL*. In this article, due to the approximate Craig interpolation property for RGL*, the Robinson theorem and approximate Beth theorem are presented and proved. Then, the omitting types theorem for this logic is...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/9/858 |
| _version_ | 1797581297041801216 |
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| author | Nazanin Roshandel Tavana |
| author_facet | Nazanin Roshandel Tavana |
| author_sort | Nazanin Roshandel Tavana |
| collection | DOAJ |
| description | Pavelka-style (rational) Gödel logic is an extension of Gödel logic which is denoted by RGL*. In this article, due to the approximate Craig interpolation property for RGL*, the Robinson theorem and approximate Beth theorem are presented and proved. Then, the omitting types theorem for this logic is expressed and proved. At the end, as a reduction, the omitting types theorem for standard Gödel logic with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula> is studied. |
| first_indexed | 2024-03-10T23:02:22Z |
| format | Article |
| id | doaj.art-5626a390f7894bb1b03c8bf998cbc292 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T23:02:22Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5626a390f7894bb1b03c8bf998cbc2922023-11-19T09:32:42ZengMDPI AGAxioms2075-16802023-09-0112985810.3390/axioms12090858Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with ΔNazanin Roshandel Tavana0Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 11366, IranPavelka-style (rational) Gödel logic is an extension of Gödel logic which is denoted by RGL*. In this article, due to the approximate Craig interpolation property for RGL*, the Robinson theorem and approximate Beth theorem are presented and proved. Then, the omitting types theorem for this logic is expressed and proved. At the end, as a reduction, the omitting types theorem for standard Gödel logic with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula> is studied.https://www.mdpi.com/2075-1680/12/9/858Robinson consistency theoremBeth theoremomitting types theoremrational Gödel logicGödel logic with Δ |
| spellingShingle | Nazanin Roshandel Tavana Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with Δ Axioms Robinson consistency theorem Beth theorem omitting types theorem rational Gödel logic Gödel logic with Δ |
| title | Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with Δ |
| title_full | Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with Δ |
| title_fullStr | Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with Δ |
| title_full_unstemmed | Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with Δ |
| title_short | Some Model Theoretic Properties for Pavelka-Style Gödel Logic, RGL* and Gödel Logic with Δ |
| title_sort | some model theoretic properties for pavelka style godel logic rgl and godel logic with δ |
| topic | Robinson consistency theorem Beth theorem omitting types theorem rational Gödel logic Gödel logic with Δ |
| url | https://www.mdpi.com/2075-1680/12/9/858 |
| work_keys_str_mv | AT nazaninroshandeltavana somemodeltheoreticpropertiesforpavelkastylegodellogicrglandgodellogicwithd |