In mathematics, Robinson arithmetic, or Q, is a finitely axiomatized fragment of Peano arithmetic (PA), first set out in R. M. Robinson (1950). Q is essentially PA without the axiom schema of induction. Since Q is weaker than PA, it is incomplete. Q is important and interesting because it is a finitely axiomatized fragment of PA that is recursively incompletable and essentially undecidable.
Read more about Robinson Arithmetic: Axioms, Metamathematics
Famous quotes containing the words robinson and/or arithmetic:
“The movies were my textbooks for everything else in the world. When it wasn’t, I altered it. If I saw a college, I would see only cheerleaders or blonds. If I saw New York City, I would want to go to the slums I’d seen in the movies, where the tough kids played. If I went to Chicago, I’d want to see the brawling factories and the gangsters.”
—Jill Robinson (b. 1936)
“‘Tis no extravagant arithmetic to say, that for every ten jokes,—thou hast got an hundred enemies; and till thou hast gone on, and raised a swarm of wasps about thine ears, and art half stung to death by them, thou wilt never be convinced it is so.”
—Laurence Sterne (1713–1768)