filtration

A filtration is a sequence of sets $A_1,A_2,\mathrm{\dots },A_n$ with

$$A_1\subset A_2\subset \mathrm{\cdots }\subset A_n.$$

If one considers the sets $A_1,\mathrm{\dots },A_n$ as elements of a larger set which are partially ordered by inclusion, then a filtration is simply a finite chain with respect to this partial ordering. It should be noted that in some contexts the word “filtration” may also be employed to describe an infinite chain.