Robinson Arithmetic

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:

    Like a wild stranger out of wizard-land
    He dwelt a little with us, and withdrew;
    Black and unblossomed were the ways he knew,
    Dark was the glass through which his fire eye shined.
    —Edwin Arlington Robinson (1869–1935)

    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 (1803–1882)