The HOD Dichotomy

TL;DR

This paper introduces the HOD conjecture, explores its equivalence to weak extender models for supercompactness, and discusses its implications in set theory, providing an accessible overview of Woodin's work.

Contribution

It establishes the equivalence of the HOD conjecture with weak extender models for supercompactness and explores its consequences, making Woodin's work more accessible.

Findings

HOD conjecture is equivalent to a formulation involving weak extender models

The paper discusses consequences of the HOD conjecture in set theory

Provides an accessible introduction to Woodin's work on extender models

Abstract

This paper provides an accessible introduction to some of the work of Woodin on suitable extender models. We define the HOD conjecture, prove it is equivalent to a formulation in terms of weak extender models for supercompactness, and give some of its consequences.