# Difference between revisions of "Nearly supercompact"

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− | {{DISPLAYTITLE: Nearly $\theta$- | + | {{DISPLAYTITLE: Nearly $\theta$-supercompact cardinals}} |

A cardinal $\kappa$ is ''nearly $\theta$-supercompact'' if and only if every family $A\subset P_\kappa\theta$ of size $\theta$ has a normal fine $\kappa$-complete filter measuring every set in $A$. | A cardinal $\kappa$ is ''nearly $\theta$-supercompact'' if and only if every family $A\subset P_\kappa\theta$ of size $\theta$ has a normal fine $\kappa$-complete filter measuring every set in $A$. |

## Revision as of 10:02, 3 January 2012

A cardinal $\kappa$ is *nearly $\theta$-supercompact* if and only if every family $A\subset P_\kappa\theta$ of size $\theta$ has a normal fine $\kappa$-complete filter measuring every set in $A$.

This notion was introduced by Jason Schanker in his dissertation (citation needed).