Abstract: After a short introduction to the notion of E-rings we will focus on the construction of absolute E-rings, i.e., of E-rings that remain E-rings in any generic extension. We will show that the first \omega- Erd"os cardinal \kappa(\omega) is a natural bound for the existence of such absolute objects: For any cardinal \lambda < \kappa we will give the construction of an absolute E-ring of cardinality \lambda and show that there are no absolute E-rings of cardinality \kappa(\omega) or bigger. This talk will be based on a dual result from S. Shelah on the existence of absolute rigid colored trees and focus on the coding of such trees into more complex algebraic structures.