Existence Property Implies Disjunction Property
To prove the numerical existence property implies the disjunction property is trivial since a disjunction can be written as an existential formula,
- .
Therefore, assuming the numerical existence property, if is a theorem of, so is, by the numerical existence property there exists some such that is a theorem. Since is a numerial, we can check the value of, if then is a theorem and if then is a theorem, and the disjunction property is satisfied.
Read more about this topic: Disjunction And Existence Properties
Famous quotes containing the words existence, property and/or implies:
“The very existence of government at all, infers inequality. The citizen who is preferred to office becomes the superior to those who are not, so long as he is the repository of power, and the child inherits the wealth of the parent as a controlling law of society.”
—James Fenimore Cooper (1789–1851)
“The awareness of the all-surpassing importance of social groups is now general property in America.”
—Johan Huizinga (1872–1945)
“Begin with loss and see
how the world contradicts you,
how the horizon implies that beyond it
the water is not empty
but full of ships
all docking at another island.”
—Lynn Emanuel (b. 1949)