Relationship To Provability
The result that MU cannot be obtained with these rules demonstrates the notion of independence in mathematical logic. The MIU system can be viewed as a formal logic in which a string is considered provable if it can be derived by application of the rules starting from MI. In this interpretation, the question is phrased as "Is MU provable in the MIU logic?".
Finding an invariant of the inference rules is a common method for establishing independence results.
Read more about this topic: MU Puzzle
Famous quotes containing the words relationship to and/or relationship:
“Sometimes in our relationship to another human being the proper balance of friendship is restored when we put a few grains of impropriety onto our own side of the scale.”
—Friedrich Nietzsche (1844–1900)
“Christianity as an organized religion has not always had a harmonious relationship with the family. Unlike Judaism, it kept almost no rituals that took place in private homes. The esteem that monasticism and priestly celibacy enjoyed implied a denigration of marriage and parenthood.”
—Beatrice Gottlieb, U.S. historian. The Family in the Western World from the Black Death to the Industrial Age, ch. 12, Oxford University Press (1993)