Generalized Cardinal Properties of Lattices and Lattice Ordered Groups

Abstract

We denote by K the class of all cardinals; put K′ = K ⋃ {α}. Let be a class of algebraic systems. A generalized cardinal property f on is defined to be a rule which assings to each A ∈ an element fA of K′ such that, whenever A₁, A₂ ∈ and A₁ ≃ A₂, then fA ₁ = fA ₂. In this paper we are interested mainly in the cases when (i) is the class of all bounded lattices B having more than one element, or (ii) is a class of lattice ordered groups.