Turing Degree - Basic Properties of The Turing Degrees

Basic Properties of The Turing Degrees

  • Every Turing degree is countably infinite, that is, it contains exactly sets.
  • There are distinct Turing degrees.
  • For each degree a the strict inequality a < a′ holds.
  • For each degree a, the set of degrees below a is at most countable. The set of degrees greater than a has size .

Read more about this topic:  Turing Degree

Famous quotes containing the words basic, properties and/or degrees:

    “It is easier to move rivers and mountains than to change a person’s basic nature.”
    —Chinese proverb.

    “The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
    —John Locke (1632–1704)

    “I was by degrees awakened as from a dream, and feared that my whole life could properly be counted nothing else but a fantastic vision.”
    —Sarah Fielding (1710–1768)