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The Jackson analysis and the strongest hypotheses

By Gabriel Goldberg

Appears in collection : XVI International Luminy Workshop in Set Theory / XVI Atelier international de théorie des ensembles

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.

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Citation data

  • DOI 10.24350/CIRM.V.19809403
  • Cite this video Goldberg Gabriel (9/13/21). The Jackson analysis and the strongest hypotheses. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19809403
  • URL https://dx.doi.org/10.24350/CIRM.V.19809403



  • Goldberg, Gabriel. "Even ordinals and the Kunen inconsistency." arXiv preprint arXiv:2006.01084 (2020). - https://arxiv.org/abs/2006.01084
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  • 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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