A field of study attempting to exhaustively describe a particular class of constructs.
“Knot theory classifies the mappings of a circle into 3-space.”
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).