$\kappa$-complete

A structured set $S$ (typically a filter or a Boolean algebra) is $\kappa$-complete if, given any $K\subseteq S$ with , $\bigcap K\in S$. It is complete if it is $\kappa$-complete for all $\kappa$.

Similarly, a partial order is $\kappa$-complete if any sequence of fewer than $\kappa$ elements has an upper bound within the partial order.

A ${\mathrm{\aleph }}_1$-complete is called countably complete.

Title	$\kappa$-complete
Canonical name	kappacomplete
Date of creation	2013-03-22 12:53:07
Last modified on	2013-03-22 12:53:07
Owner	Henry (455)
Last modified by	Henry (455)
Numerical id	11
Author	Henry (455)
Entry type	Definition
Classification	msc 03E10
Synonym	kappa-complete
Synonym	kappa complete
Related topic	Filter
Related topic	BooleanAlgebra
Defines	countably complete