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H 1 Towards the right generalization of descriptive set theory to uncountable cardinals

Auteurs : Motto Ros, Luca (Auteur de la Conférence)
CIRM (Editeur )

Résumé : Generalized descriptive set theory has mostly been developed for uncountable cardinals satisfying the condition $\kappa ^{< \kappa }=\kappa$ (thus in particular for $\kappa$ regular). More recently the case of uncountable cardinals of countable cofinality has attracted some attention, partially because of its connections with very large cardinal axioms like I0. In this talk I will survey these recent developments and propose a unified approach which potentially could encompass all possible scenarios (including singular cardinals of arbitrary cofinality).

Keywords : generalized descriptive set theory; large cardinals, Choquet-like spaces

Codes MSC :
03E15 - Descriptive set theory
03E55 - Large cardinals
54A05 - Topological spaces and generalizations (closure spaces, etc.)

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2052/Slides/Motto-Ross-190926Luminy_handout.pdf

 Informations sur la Vidéo Réalisateur : Recanzone, Luca Langue : Anglais Date de publication : 14/10/2019 Date de captation : 25/09/2019 Collection : Research talks ; Logic and Foundations Format : MP4 Durée : 00:51:59 Domaine : Logic and Foundations Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2019-09-26_Ros.mp4 Informations sur la rencontre Nom de la rencontre : 15th International Luminy Workshop in Set Theory / XVe Atelier international de théorie des ensemblesOrganisateurs de la rencontre : Dzamonja, Mirna ; Velickovic, BobanDates : 23/09/2019 - 27/09/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2052.htmlCitation Data DOI : 10.24350/CIRM.V.19564203 Cite this video as: Motto Ros, Luca (2019). Towards the right generalization of descriptive set theory to uncountable cardinals. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19564203 URI : http://dx.doi.org/10.24350/CIRM.V.19564203

### Voir aussi

Bibliographie

1. KECHRIS, Alexander. Classical descriptive set theory. Graduate texts in mathematics 156, 2012. -

2. STONE, Arthur Harold. Non-separable Borel sets. General Topology and its Relations to Modern Analysis and Algebra, 1962, p. [341]-342. - https://dml.cz/bitstream/handle/10338.dmlcz/700949/Toposym_01-1961-1_84.pdf

3. WOODIN, W. Hugh. Suitable extender models II: beyond ω-huge. Journal of Mathematical Logic, 2011, vol. 11, no 02, p. 115-436. - https://doi.org/10.1142/S021906131100102X

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