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:

    Never mind if you fall far short of the thing you want to do,—encourage your effort. If no one else will say it to you, say it to yourself. “Not so bad.” It will make the next effort easier and better.
    —Josephine Demott Robinson (1865–1948)

    O! O! another stroke! that makes the third.
    He stabs me to the heart against my wish.
    If that be so, thy state of health is poor;
    But thine arithmetic is quite correct.
    —A.E. (Alfred Edward)