Formulas and Properties, Their Links and Characteristics
In this work, we study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to the given properties are described. Characteristics of generic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1391 |
| _version_ | 1797530079206572032 |
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| author | Sergey V. Sudoplatov |
| author_facet | Sergey V. Sudoplatov |
| author_sort | Sergey V. Sudoplatov |
| collection | DOAJ |
| description | In this work, we study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to the given properties are described. Characteristics of generic sentences and generic theories with respect to these properties are described and characterized. |
| first_indexed | 2024-03-10T10:23:50Z |
| format | Article |
| id | doaj.art-cd773d35fc2b467c9266ba6a38880d23 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:23:50Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cd773d35fc2b467c9266ba6a38880d232023-11-22T00:13:29ZengMDPI AGMathematics2227-73902021-06-01912139110.3390/math9121391Formulas and Properties, Their Links and CharacteristicsSergey V. Sudoplatov0Sobolev Institute of Mathematics, Academician Koptyug Ave., 4, 630090 Novosibirsk, RussiaIn this work, we study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to the given properties are described. Characteristics of generic sentences and generic theories with respect to these properties are described and characterized.https://www.mdpi.com/2227-7390/9/12/1391formulapropertyrankdegreegeneric sentencegeneric theory |
| spellingShingle | Sergey V. Sudoplatov Formulas and Properties, Their Links and Characteristics Mathematics formula property rank degree generic sentence generic theory |
| title | Formulas and Properties, Their Links and Characteristics |
| title_full | Formulas and Properties, Their Links and Characteristics |
| title_fullStr | Formulas and Properties, Their Links and Characteristics |
| title_full_unstemmed | Formulas and Properties, Their Links and Characteristics |
| title_short | Formulas and Properties, Their Links and Characteristics |
| title_sort | formulas and properties their links and characteristics |
| topic | formula property rank degree generic sentence generic theory |
| url | https://www.mdpi.com/2227-7390/9/12/1391 |
| work_keys_str_mv | AT sergeyvsudoplatov formulasandpropertiestheirlinksandcharacteristics |