# Difference between revisions of "Axiom of constructibility"

From Cantor's Attic

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− | {{DISPLAYTITLE: V = L}} | + | {{DISPLAYTITLE: The axiom of constructibility, $V = L$}} |

− | $V = L$ | + | The axiom of constructibility, written $V=L$, is the assertion that the universe of all sets is exactly the universe of all constructible sets. It is minimalistic in the sense that any inner model $M$ of ZF must contain all sets from Gödel's constructible universe $L$. The axiom is compatible with some of the smaller large cardinal notions such as weak compactness but is ''not'' compatible with any large cardinal notion implying the existence of [[Zero_sharp|$0^{\sharp}$]] such as measurability. |

{{stub}} | {{stub}} |

## Revision as of 04:55, 3 January 2012

The axiom of constructibility, written $V=L$, is the assertion that the universe of all sets is exactly the universe of all constructible sets. It is minimalistic in the sense that any inner model $M$ of ZF must contain all sets from Gödel's constructible universe $L$. The axiom is compatible with some of the smaller large cardinal notions such as weak compactness but is *not* compatible with any large cardinal notion implying the existence of $0^{\sharp}$ such as measurability.

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