Full Idea
Henkin semantics (for second-order logic) specifies a second domain of predicates and relations for the upper case constants and variables.
Gist of Idea
Henkin semantics has a second domain of predicates and relations (in upper case)
Source
Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3)
A Reaction
This second domain is restricted to predicates and relations which are actually instantiated in the model. Second-order logic is complete with this semantics. Cf. Idea 10756.
Related Idea
Idea 10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]