(logic) A procedure for "discharging" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form P,A⊢C to an inference of the form P⊢A→C or vice versa, where ⊢ is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory.

(mathematics) A theorem stating that every Goodstein sequence eventually terminates at zero.

plural of scallop theorem

A theorem postulating that all black hole solutions of the Einstein-Maxwell equations in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum.

(mathematics) a theorem providing conditions under which an operator or matrix can be diagonalized

(probability theory) A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event.

(algebraic geometry) A theorem stating that a normal algebraic variety with an action of a torus can be covered by torus-invariant affine open subsets.

(mathematics) A result in combinatorics, stating that every set of integers with positive natural density contains a k-term arithmetic progression for every k.

(mathematics) A theorem proving that it is always possible to tile a chessboard with dominoes if two squares of opposite colors are first removed from the board.

(logic) A fundamental result of mathematical logic, essentially allowing a certain kind of reduction of first-order logic to propositional logic.