The exact consistency strength of the generic absoluteness for the universally Baire sets
A set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property. $\mathsf {Sealing}$ is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be chang...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423001275/type/journal_article |
| _version_ | 1797352352955498496 |
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| author | Grigor Sargsyan Nam Trang |
| author_facet | Grigor Sargsyan Nam Trang |
| author_sort | Grigor Sargsyan |
| collection | DOAJ |
| description | A set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property.
$\mathsf {Sealing}$
is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be changed by forcing. |
| first_indexed | 2024-03-08T13:14:14Z |
| format | Article |
| id | doaj.art-50d8d08a9c78452aa4db253186d92017 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-03-08T13:14:14Z |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-50d8d08a9c78452aa4db253186d920172024-01-18T08:51:13ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2023.127The exact consistency strength of the generic absoluteness for the universally Baire setsGrigor Sargsyan0https://orcid.org/0000-0002-6095-1997Nam Trang1Institute of Mathematics of Polish Academy of Sciences, Poland; E-mail:Department of Mathematics, University of North Texas, Denton, TX, USA; E-mail:A set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property. $\mathsf {Sealing}$ is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be changed by forcing.https://www.cambridge.org/core/product/identifier/S2050509423001275/type/journal_article |
| spellingShingle | Grigor Sargsyan Nam Trang The exact consistency strength of the generic absoluteness for the universally Baire sets Forum of Mathematics, Sigma |
| title | The exact consistency strength of the generic absoluteness for the universally Baire sets |
| title_full | The exact consistency strength of the generic absoluteness for the universally Baire sets |
| title_fullStr | The exact consistency strength of the generic absoluteness for the universally Baire sets |
| title_full_unstemmed | The exact consistency strength of the generic absoluteness for the universally Baire sets |
| title_short | The exact consistency strength of the generic absoluteness for the universally Baire sets |
| title_sort | exact consistency strength of the generic absoluteness for the universally baire sets |
| url | https://www.cambridge.org/core/product/identifier/S2050509423001275/type/journal_article |
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