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“The manufacturing corporation, except in comparatively few instances, no longer represents a protecting care, a parental influence, over its operatives. It is too often a soulless organization; and its members forget that they are morally responsible for the souls and bodies, as well as for the wages, of those whose labor is the source of their wealth.”
—Harriet H. Robinson (18251911)
“Under the dominion of an idea, which possesses the minds of multitudes, as civil freedom, or the religious sentiment, the power of persons are no longer subjects of calculation. A nation of men unanimously bent on freedom, or conquest, can easily confound the arithmetic of statists, and achieve extravagant actions, out of all proportion to their means; as, the Greeks, the Saracens, the Swiss, the Americans, and the French have done.”
—Ralph Waldo Emerson (18031882)