On $\omega $ -Strongly Measurable Cardinals
We prove several consistency results concerning the notion of $\omega $ -strongly measurable cardinal in $\operatorname {\mathrm {HOD}}$ . In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than $o(\kappa ) = \kappa $ , that every successor...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423000154/type/journal_article |
| _version_ | 1797870456429084672 |
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| author | Omer Ben-Neria Yair Hayut |
| author_facet | Omer Ben-Neria Yair Hayut |
| author_sort | Omer Ben-Neria |
| collection | DOAJ |
| description | We prove several consistency results concerning the notion of
$\omega $
-strongly measurable cardinal in
$\operatorname {\mathrm {HOD}}$
. In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than
$o(\kappa ) = \kappa $
, that every successor of a regular cardinal is
$\omega $
-strongly measurable in
$\operatorname {\mathrm {HOD}}$
. |
| first_indexed | 2024-04-10T00:27:47Z |
| format | Article |
| id | doaj.art-7816d850975e41b3ace984f01ba7514d |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T00:27:47Z |
| publishDate | 2023-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-7816d850975e41b3ace984f01ba7514d2023-03-15T06:00:07ZengCambridge University PressForum of Mathematics, Sigma2050-50942023-01-011110.1017/fms.2023.15On $\omega $ -Strongly Measurable CardinalsOmer Ben-Neria0https://orcid.org/0000-0003-1277-9384Yair Hayut1https://orcid.org/0000-0002-3805-7446The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Givat Ram, Jerusalem, 91904, Israel; E-mail:The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Givat Ram, Jerusalem, 91904, Israel; E-mail:We prove several consistency results concerning the notion of $\omega $ -strongly measurable cardinal in $\operatorname {\mathrm {HOD}}$ . In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than $o(\kappa ) = \kappa $ , that every successor of a regular cardinal is $\omega $ -strongly measurable in $\operatorname {\mathrm {HOD}}$ .https://www.cambridge.org/core/product/identifier/S2050509423000154/type/journal_article03E4503E3503E55 |
| spellingShingle | Omer Ben-Neria Yair Hayut On $\omega $ -Strongly Measurable Cardinals Forum of Mathematics, Sigma 03E45 03E35 03E55 |
| title | On $\omega $ -Strongly Measurable Cardinals |
| title_full | On $\omega $ -Strongly Measurable Cardinals |
| title_fullStr | On $\omega $ -Strongly Measurable Cardinals |
| title_full_unstemmed | On $\omega $ -Strongly Measurable Cardinals |
| title_short | On $\omega $ -Strongly Measurable Cardinals |
| title_sort | on omega strongly measurable cardinals |
| topic | 03E45 03E35 03E55 |
| url | https://www.cambridge.org/core/product/identifier/S2050509423000154/type/journal_article |
| work_keys_str_mv | AT omerbenneria onomegastronglymeasurablecardinals AT yairhayut onomegastronglymeasurablecardinals |