English

The internal structure of $\mathrm{HOD}^{L[x]}$ up to its Woodin

Logic 2017-11-09 v2

Abstract

Assume Δ31\boldsymbol{\Delta}^1_3-determinacy. It is shown that for any xTM1#x \geq_T M_1^{\#}, HODL[x]\mathrm{HOD}^{L[x]} is a model of GCH, and in fact, it is a Jensen-Steel core model up to ω2L[x]\omega_2^{L[x]}.

Keywords

Cite

@article{arxiv.1711.02007,
  title  = {The internal structure of $\mathrm{HOD}^{L[x]}$ up to its Woodin},
  author = {Yizheng Zhu},
  journal= {arXiv preprint arXiv:1711.02007},
  year   = {2017}
}

Comments

withdrawn due to a mistake in Lemma 6.2