Theory

- Natural & Formal Sciences -
Mathematics & Logic Dictionary
Definition
A collection of formulas in a formal language taken as a body of statements, often presented as a set of axioms together with all formulas derivable from them; a theory can be finite or infinite, axiomatizable or defined by its set of models.

Theory

- Pure Mathematics -
Algebra Dictionary
Definition
A collection of sentences in a fixed logical language, typically closed under logical consequence, whose members serve as axioms or consequences that characterize a class of models.