Abstract
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 
-supercompact”. Our proof uses inner model theoretic tools instead of Baire category. We also show that \(\omega _2\) is \(<\Theta \)-strongly compact.
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Sargsyan, G. An inner model theoretic proof of Becker’s theorem. Arch. Math. Logic 58, 999–1003 (2019). https://doi.org/10.1007/s00153-019-00668-9
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DOI: https://doi.org/10.1007/s00153-019-00668-9