Disjunction Property Implies Existence Property
In 1974 Harvey Friedman proved that in any recursively enumerable extension of intuitionistic arithmetic, the converse of the above also holds. Throughout the following discussion assume is such an extension of arithmetic. Harvey Friedman's proof is quite intricate, making of self-referential sentences in a similar way to the one used in the proof of the incompleteness theorem. They key step is to find a bound on the existential quantifier because bounded existential formula can be written as a disjunction,
- .
However, given an arbitrary existential formula, can we hope to replace it by a bounded one?
Read more about this topic: Disjunction And Existence Properties
Famous quotes containing the words property, implies and/or existence:
“I must feel pride in my friend’s accomplishments as if they were mine,—and a property in his virtues. I feel as warmly when he is praised, as the lover when he hears applause of his engaged maiden.”
—Ralph Waldo Emerson (1803–1882)
“The pure work implies the disappearance of the poet as speaker, who hands over to the words.”
—Stéphane Mallarmé (1842–1898)
“As humans have a prior right to existence over dogs by virtue of being more highly evolved and having a superior consciousness, so women have a prior right to existence over men. The elimination of any male is, therefore, a righteous and good act, an act highly beneficial to women as well as an act of mercy.”
—Valerie Solanas (b. 1940)