Ultraproducts and Related Constructions
In this work, we survey some research directions in which the ultraproduct construction and methods based on ultrafilters play significant roles. Rather different areas of mathematics have been considered: topics we are reviewing here include some aspects of the model theory of first-order and secon...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/1/70 |
| _version_ | 1797625350992166912 |
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| author | Gábor Sági |
| author_facet | Gábor Sági |
| author_sort | Gábor Sági |
| collection | DOAJ |
| description | In this work, we survey some research directions in which the ultraproduct construction and methods based on ultrafilters play significant roles. Rather different areas of mathematics have been considered: topics we are reviewing here include some aspects of the model theory of first-order and second-order existential logics, finite Ramsey theory and general topology. Special emphasis has been made for producing a uniform treatment and for highlighting interconnections between these different subjects. |
| first_indexed | 2024-03-11T09:55:20Z |
| format | Article |
| id | doaj.art-b9e6963c5ff842ea995e88888cf19ba3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:55:20Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b9e6963c5ff842ea995e88888cf19ba32023-11-16T15:53:04ZengMDPI AGMathematics2227-73902022-12-011117010.3390/math11010070Ultraproducts and Related ConstructionsGábor Sági0Alfréd Rényi Institute of Mathematics, P.O. Box 127, H-1364 Budapest, HungaryIn this work, we survey some research directions in which the ultraproduct construction and methods based on ultrafilters play significant roles. Rather different areas of mathematics have been considered: topics we are reviewing here include some aspects of the model theory of first-order and second-order existential logics, finite Ramsey theory and general topology. Special emphasis has been made for producing a uniform treatment and for highlighting interconnections between these different subjects.https://www.mdpi.com/2227-7390/11/1/70ultrafilterultraproductfirst order logicsecond order logicfinite Ramsey theoryultraproducts in general topology |
| spellingShingle | Gábor Sági Ultraproducts and Related Constructions Mathematics ultrafilter ultraproduct first order logic second order logic finite Ramsey theory ultraproducts in general topology |
| title | Ultraproducts and Related Constructions |
| title_full | Ultraproducts and Related Constructions |
| title_fullStr | Ultraproducts and Related Constructions |
| title_full_unstemmed | Ultraproducts and Related Constructions |
| title_short | Ultraproducts and Related Constructions |
| title_sort | ultraproducts and related constructions |
| topic | ultrafilter ultraproduct first order logic second order logic finite Ramsey theory ultraproducts in general topology |
| url | https://www.mdpi.com/2227-7390/11/1/70 |
| work_keys_str_mv | AT gaborsagi ultraproductsandrelatedconstructions |