*This page is aimed to be a collection of many results from papers, slides/presentation, etc. about Woodin's Ultimate L, HOD Conjecture, $\Omega$-conjecture, and other similar topics. I do intend this page to serve as a base for an article or more. Any suggestion is welcome.*

Throughout this page, we will use $\text{ZFW}$ to denote $\text{ZFC+}$"there is a proper class of Woodin cardinals".

## Contents

- 1 Projective sets, determinacy, $\Omega$-logic, $\Omega$-conjecture, Continuum Hypothesis
- 2 $L(\R)$, Universally Baire sets, Weak extender models, $\omega$-strong measurability, $\text{HOD}$ dichotomy
- 3 $\text{AD}^+$, Ultimate $L$, Conjectures
- 4 Suitable extender models, rank-into-rank cardinals

## Projective sets, determinacy, $\Omega$-logic, $\Omega$-conjecture, Continuum Hypothesis

## $L(\R)$, Universally Baire sets, Weak extender models, $\omega$-strong measurability, $\text{HOD}$ dichotomy

## $\text{AD}^+$, Ultimate $L$, Conjectures

## Suitable extender models, rank-into-rank cardinals