An inner model theoretic proof of Becker’s theorem

  • Grigor SargsyanEmail author


We re-prove Becker’s theorem from Becker (Isr J Math 40(3–4):229–234, 1981) by showing that \(AD^{L({\mathbb {R}})}\) implies that \(L({\mathbb {R}})\vDash ``\omega _2\) is Open image in new window -supercompact”. Our proof uses inner model theoretic tools instead of Baire category. We also show that \(\omega _2\) is \(<\Theta \)-strongly compact.


Set theory Inner model theory Directed systems Descriptive set theory 

Mathematics Subject Classification

03E15 03E35 03E45 03E55 03E57 03E60 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Rutgers The State University of New JerseyNew BrunswickUSA

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