Actualist models satisfying N_Q can systematically differ from SQML's Kripkean constant-domain semantics in how they interpret the inner domain, preserving a real distinction Linsky and Zalta have defended.

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Actualist models(in modal logic and metaphysics): A way of thinking about what's real that says only things that actually exist matter; contrasts with views that also count things that could exist but don't.
Inner domain(in formal semantics): In logic, the set of things that count as 'really existing' in a particular model or scenario, as opposed to things that merely might exist.
Kripkean constant-domain semantics(in modal logic): A method developed by philosopher Saul Kripke for understanding how logic works when we talk about what's possible and necessary; 'constant-domain' means we assume the same objects exist in all possible scenarios.
Linsky and Zalta(in metaphysics and philosophy of logic): Bernard Linsky and Edward Zalta are contemporary philosophers who have written about what exists and how logic should handle abstract objects like fictional characters.

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