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Full Idea
A theory is a set of formulae closed under first-order logical consequence.
Gist of Idea
A theory is some formulae and all of their consequences
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 5.1)
Book Ref
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.29