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The Jackson analysis and the strongest hypotheses
Multi angle
Authors : Goldberg, Gabriel (Author of the conference)
CIRM (Publisher )
03E05 - Combinatorial set theory (logic)
03E45 - Constructibility, ordinal definability, and related notions
03E55 - Large cardinals
03E60 - Determinacy principles
Additional resources :
https://www.cirm-math.fr/RepOrga/2370/Slides/Goldberg.pdf
CIRM (Publisher )
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Abstract :
In his work on the projective ordinals, Jackson initiated a detailed analysis of the structure of the cardinal numbers in the inner model L(R). To complete this analysis seems to require the development of a global theory of measures on ordinals in L(R). We present some results in this direction which are inspired by the unexplained analogy between the Axiom of Determinacy and the strongest large cardinal hypotheses.
Keywords : Ultrapower Axiom; I0; determinacy; ultrafilter
MSC Codes : Keywords : Ultrapower Axiom; I0; determinacy; ultrafilter
03E05 - Combinatorial set theory (logic)
03E45 - Constructibility, ordinal definability, and related notions
03E55 - Large cardinals
03E60 - Determinacy principles
Additional resources :
https://www.cirm-math.fr/RepOrga/2370/Slides/Goldberg.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/10/2021 Conference Date : 13/09/2021 Subseries : Research talks arXiv category : Logic Mathematical Area(s) : Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:05:14 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-13_Goldberg.mp4 
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Information on the Event
Event Title : XVI International Luminy Workshop in Set Theory / XVI Atelier international de théorie des ensemblesEvent Organizers : Fischer, Vera ; Velickovic, Boban ; Viale, Matteo Dates : 13/09/2021 - 17/09/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2370.html
Citation Data
DOI : 10.24350/CIRM.V.19809403Cite this video as: Goldberg, Gabriel (2021). The Jackson analysis and the strongest hypotheses. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19809403 URI : http://dx.doi.org/10.24350/CIRM.V.19809403 |
See Also
- [Multi angle] Perfect matchings in hyperfinite graphings / Author of the conference Sabok, Marcin.
- [Multi angle] Torsion-free Abelian groups are Borel complete / Author of the conference Paolini, Gianluca.
- [Multi angle] Welch games to Laver Ideals / Author of the conference Foreman, Matthew.
- [Multi angle] Universal ${ \aleph }_{2}$-Aronszajn trees / Author of the conference Dzamonja, Mirna.
Bibliography
- Goldberg, Gabriel. "Even ordinals and the Kunen inconsistency." arXiv preprint arXiv:2006.01084 (2020). - https://arxiv.org/abs/2006.01084
- Steel, John R., and W. Hugh Woodin. "HOD as a core model." Ordinal definability and recursion theory: the Cabal Seminar. Vol. 3. 2016. -
- Woodin, W. Hugh. "Suitable extender models II: beyond ω-huge." Journal of Mathematical Logic 11.02 (2011): 115-436. - https://doi.org/10.1142/S021906131100102X
- Jackson, Steve. "AD and the projective ordinals." in Kechris A.S., Martin D.A., Steel J.R. (eds) Cabal Seminar 81–85. Lecture Notes in Mathematics, vol 1333 Springer, Berlin, Heidelberg, 1988. - https://doi.org/10.1007/BFb0084974
- Cramer, Scott. "Implications of very large cardinals." in Caicedo, Andrés Eduardo, et al., eds. Foundations of Mathematics. Contemporary Mathematics 690 (2017): 225-257.American Mathematical Soc., 2017. - https://www.ams.org/books/conm/690/13870
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