We display the entire structure R2 coding Σ1- and
Σ2-elementarity on the ordinals. This will enable the analysis of pure
Σ3-elementary substructures.Comment: Extensive rewrite of the introduction. Mathematical content of
sections 2 and 3 unchanged, extended introduction to section 2. Removed
section 4. Theorem 4.3 to appear elsewhere with corrected proo