A filtrator is a pair (𝔄;) consisting of a poset 𝔄 (the base of the filtrator) and its subset (the core of the filtrator). The set is considered as a poset with the induced order.

Having fixed a filtrator and an a𝔄, we define:


Probably the most important example of a filtrator is a primary filtrator that is the pair (𝔉;𝔓) where 𝔉 is the set of filters on a poset ordered reverse to set-theoretic inclusion of filters and 𝔓 is the set of principal filtersPlanetmathPlanetmathPlanetmath on this poset. For a filter 𝔉 we have up essentially equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath with the set .


  • 1 Victor Porton. on posets and generalizationsPlanetmathPlanetmath. International Journal of Pure and Applied Mathematics, 74(1):55–119, 2012.
Title Filtrator
Canonical name Filtrator
Date of creation 2013-03-22 19:31:25
Last modified on 2013-03-22 19:31:25
Owner porton (9363)
Last modified by porton (9363)
Numerical id 6
Author porton (9363)
Entry type Definition
Classification msc 06B99
Classification msc 06A06
Classification msc 54A20
Related topic Filter
Related topic Filter2
Defines primary filtrator