Local Definability of $\mathsf{HOD}$ in $L(\mathbb{R})$

Obrad Kasum

Local Definability of $\mathsf{HOD}$ in $L(\mathbb{R})$

Logic 2023-08-03 v1

Authors: Obrad Kasum

Abstract

We show that in $L(\mathbb{R})$ , assuming large cardinals, $\mathsf{HOD} {\parallel}\eta^{+\mathsf{HOD}}$ is locally definable from $\mathsf{HOD} {\parallel}\eta$ for all $\mathsf{HOD}$ -cardinals $\eta\in [\boldsymbol{\delta}^2_1,\Theta)$ . This is a further elaboration of the statement " $\mathsf{HOD}^{L(\mathbb{R})}$ is a core model below $\Theta$ " made by John Steel.

Keywords

local definability hod l(r) large cardinals core model

Cite

@article{arxiv.2308.01072,
  title  = {Local Definability of $\mathsf{HOD}$ in $L(\mathbb{R})$},
  author = {Obrad Kasum},
  journal= {arXiv preprint arXiv:2308.01072},
  year   = {2023}
}

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