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:
“Sport in the sense of a mass-spectacle, with death to add to the underlying excitement, comes into existence when a population has been drilled and regimented and depressed to such an extent that it needs at least a vicarious participation in difficult feats of strength or skill or heroism in order to sustain its waning life-sense.”
—Lewis Mumford (1895–1990)
“Open the doors of opportunity to talent and virtue and they will do themselves justice, and property will not be in bad hands.”
—Ralph Waldo Emerson (1803–1882)
“A faculty for idleness implies a catholic appetite and a strong sense of personal identity.”
—Robert Louis Stevenson (1850–1894)