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A reduction system is said to posses the Church-Rosser property if, for all x and y such that x<->_*y, there exists a z such that x->_*z and y->_*z. A reduction system is ...

The Church-Rosser theorem states that lambda calculus as a reduction system with lambda conversion rules satisfies the Church-Rosser property.

Church proved several important theorems that now go by the name Church's theorem. One of Church's theorems states that there is no consistent decidable extension of Peano ...

Let x->y and u->v be two rules of a term rewriting system, and suppose these rules have no variables in common. If they do, rename the variables. If x_1 is a subterm of x (or ...

The cut elimination theorem, also called the "Hauptsatz" (Gentzen 1969), states that every sequent calculus derivation can be transformed into another derivation with the ...

In predicate calculus, an existential formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...

A reduction system is called finitely terminating (or Noetherian) if there are no infinite rewriting sequences. This property guarantees that any rewriting algorithm will ...

A purple cow is a confirming instance of the hypothesis that all crows are black.

Assume X, Y, and Z are lotteries. Denote "X is preferred to Y" as X≻Y, and indifference between them by X∼Y. One version of the probability axioms are then given by the ...

The study of the inner structure of a mathematical theory considered as a whole. It deals with the general properties of the rules according to which the objects of a certain ...