The internal structure of HOD^(L[x]) up to its Woodin
classification
🧮 math.LO
keywords
mathrmmodelassumeboldsymbolcoredeltadeterminacyfact
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Assume $\boldsymbol{\Delta}^1_3$-determinacy. It is shown that for any $x \geq_T M_1^{\#}$, $\mathrm{HOD}^{L[x]}$ is a model of GCH, and in fact, it is a Jensen-Steel core model up to $\omega_2^{L[x]}$.
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