# Difference between revisions of "HOD"

From Cantor's Attic

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− | {{DISPLAYTITLE: | + | {{DISPLAYTITLE: 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 $N$. | |

− | Although it is definable, this definition is not absolute for transitive inner models of | + | |

## Revision as of 12:37, 11 November 2017

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.

## Relativizations

## References

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