Set theory influenced logic, both through its semantics, by expanding the possible models of various theories and by the formal definition of a model; and through its syntax, by allowing for logical languages in which formulas can be infinite in length or in which the number of symbols is uncountable

Bulletin of Symbolic Logic 4 (3) (1998)
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Completeness in the theory of types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
Axiom of Choice and Complementation.Radu Diaconescu - 1975 - Proceedings of the American Mathematical Society 51 (1):176-178.
IF first-order logic and truth-definitions.Gabriel Sandu - 1997 - Journal of Philosophical Logic 26.

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