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Full Idea
Bernays (1918) formulated and proved the completeness of propositional logic, the first precise solution as part of the Hilbert programme.
Gist of Idea
Bernays (1918) formulated and proved the completeness of propositional logic
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.1)
Book Ref
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.180