Before revision: The impossibility of the Entscheidungsproblem The (German for 'decision problem') is a challenge posed by David Hilbert in 1928.Hilbert and Ackermann The asks for an algorithm that takes as input a statement of a first-order logic (possibly with a finite number of axioms beyond the usual axioms of first-order logic) and answers "Yes" or "No" according to whether the statement is universally valid, i.e., valid in every structure satisfying the axioms.
After revision: The undecidability of the Entscheidungsproblem The (German for 'decision problem') is a challenge posed by David Hilbert in 1928.Hilbert and Ackermann The asks for an algorithm that takes as input a statement of a first-order logic (possibly with a finite number of axioms beyond the usual axioms of first-order logic) and answers "Yes" or "No" according to whether the statement is universally valid, i.e., valid in every structure satisfying the axioms.