In mathematical logic, a theory is a set of sentences in a formal language. Wikipedia

A collection of sentences in a formal language. Wikipedia Disambiguation

A set of sentences in a formal language Wikipedia Disambiguation

A set of axioms together with all statements derivable from them; or, a set of statements which are deductively closed. Equivalently, a formal language plus a set of axioms (from which can then be derived theorems). The statements may be required to all be bound (i.e., to have no free variables). Wiktionary

In logic: a set of axioms and all statements derivable from them. Wiktionary (translation)