Henkin semantics permits non-standard comprehension axioms, meaning 'categoricity' within Henkin models tracks structural properties relative to those axiom schemes, not an absolute notion.

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Axiom schemes(mathematical logic and formal systems): Families of logical rules that follow a repeating pattern—like having not just one rule, but an infinite list of similar rules.
Comprehension axioms(set theory and mathematical logic): Rules in logic that let you create a set by describing what things belong in it (like saying 'the set of all even numbers').
Henkin models(Completeness Theorem for second-order logic): Models for second-order logic in which the second-order quantifiers range over some, but not necessarily all, subsets of the domain; full Henkin models are those where all subsets are included
Henkin semantics(as used in mathematical logic): A way of interpreting logical languages (created by logician Leon Henkin) that uses a more limited set of possible interpretations than the standard approach, making the logic less powerful but more practical.

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