Very true operators in effect algebras
We introduce the concept of very true operator on an effect algebra. Although an effect algebra is only partial, we define it in the way which is in accordance with traditional definitions in residuated lattices or basic algebras. This is possible if we require monotonicity as an additional condition. We prove that very true operators on effect algebras can be characterized by means of certain subsets which are conditionally complete.
very true operator effect algebra conditionally complete subset