English

Hod up to AD$_{\mathbb{R}}+\Theta$ is measurable

Logic 2021-11-15 v1

Abstract

Suppose MM is a transitive class size model of ADR+ΘAD_{\mathbb{R}}+``\Theta is regular". MM is a minimal model of ADR+ΘAD_{\mathbb{R}}+``\Theta is measurable" if (i) R,OrdM\mathbb{R}, Ord\subseteq M (ii) there is μM\mu\in M such that MμM\models ``\mu is a normal R\mathbb{R}-complete measure on Θ\Theta" and (iii) for any transitive class size NMN\subsetneq M such that RN\mathbb{R}\subseteq N, NN\models ``there is no R\mathbb{R}-complete measure on Θ\Theta". Continuing Trang's work in [8], we compute HOD of a minimal model of ADR+ΘAD_{\mathbb{R}}+``\Theta is measurable".

Keywords

Cite

@article{arxiv.2111.06452,
  title  = {Hod up to AD$_{\mathbb{R}}+\Theta$ is measurable},
  author = {Grigor Sargsyan and Rachid Atmai},
  journal= {arXiv preprint arXiv:2111.06452},
  year   = {2021}
}