# cantors-attic

Climb into Cantor’s Attic, where you will find infinities large and small. We aim to provide a comprehensive resource of information about all notions of mathematical infinity.

View the Project on GitHub neugierde/cantors-attic

# HOD

HOD denotes the class of Hereditarily Ordinal Definable sets. It is a definable canonical inner model of ZFC.

Although it is definable, this definition is not absolute for transitive inner models of ZF, i.e. given two models $M$ and $N$ of $ZF$, $HOD$ as computed in $M$ may differ from $HOD$ as computed in $N$.

## Ordinal Definable Sets

Elements of $OD$ are all definable from a finite collection of ordinals.

## gHOD

Generic HOD (gHOD) is the intersection of HODs of all set-generic extensions of $V$. (Fuchs et al., 2015)