Characterization of Partial Lattices on Countable Boolean Lattice

Abstract

In this paper new concepts countable join property, countable meet property, Plattice and P -lattice are introduced. We established that P -lattice and P -lattice are measureable partial lattices and characterized partial lattices of a lattice through countable join and meet properties. We also established some interesting result on the injective property of the lattice measurable functions defined over countable Boolean lattices.