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Full Idea
In model theory we are interested in allowing a slightly unusual semantics for quantifiers: we are willing to allow that the quantifier not range over everything.
Gist of Idea
Model theory is unusual in restricting the range of the quantifiers
Source
Hartry Field (Tarski's Theory of Truth [1972], n 5)
Book Ref
'The Nature of Truth', ed/tr. Lynch, Michael P. [MIT 2001], p.394