Grothendieck Universes
The foundation of the Mizar Mathematical Library [2], is first-order Tarski-Grothendieck set theory. However, the foundation explicitly refers only to Tarski’s Axiom A, which states that for every set X there is a Tarski universe U such that X ∈ U. In this article, we prove, using the Mizar [3] form...
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| Format: | Article |
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Sciendo
2020-07-01
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| Series: | Formalized Mathematics |
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| Online Access: | https://doi.org/10.2478/forma-2020-0018 |
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doaj-2ef4094621bc41909dd5972ec3f59c992021-09-05T21:01:04ZengSciendoFormalized Mathematics1426-26301898-99342020-07-0128221121510.2478/forma-2020-0018forma-2020-0018Grothendieck UniversesPąk Karol0Institute of Informatics, University of Białystok, PolandThe foundation of the Mizar Mathematical Library [2], is first-order Tarski-Grothendieck set theory. However, the foundation explicitly refers only to Tarski’s Axiom A, which states that for every set X there is a Tarski universe U such that X ∈ U. In this article, we prove, using the Mizar [3] formalism, that the Grothendieck name is justified. We show the relationship between Tarski and Grothendieck universe.https://doi.org/10.2478/forma-2020-0018tarski-grothendieck set theorytarski’s axiom agrothendieck universe03e7068v20 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Pąk Karol |
| spellingShingle |
Pąk Karol Grothendieck Universes Formalized Mathematics tarski-grothendieck set theory tarski’s axiom a grothendieck universe 03e70 68v20 |
| author_facet |
Pąk Karol |
| author_sort |
Pąk Karol |
| title |
Grothendieck Universes |
| title_short |
Grothendieck Universes |
| title_full |
Grothendieck Universes |
| title_fullStr |
Grothendieck Universes |
| title_full_unstemmed |
Grothendieck Universes |
| title_sort |
grothendieck universes |
| publisher |
Sciendo |
| series |
Formalized Mathematics |
| issn |
1426-2630 1898-9934 |
| publishDate |
2020-07-01 |
| description |
The foundation of the Mizar Mathematical Library [2], is first-order Tarski-Grothendieck set theory. However, the foundation explicitly refers only to Tarski’s Axiom A, which states that for every set X there is a Tarski universe U such that X ∈ U. In this article, we prove, using the Mizar [3] formalism, that the Grothendieck name is justified. We show the relationship between Tarski and Grothendieck universe. |
| topic |
tarski-grothendieck set theory tarski’s axiom a grothendieck universe 03e70 68v20 |
| url |
https://doi.org/10.2478/forma-2020-0018 |
| work_keys_str_mv |
AT pakkarol grothendieckuniverses |
| _version_ |
1717781690110181376 |