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:
“Abscond. To “move” in a mysterious way, commonly with the property of another.”
—Ambrose Bierce (1842–1914)
“The best chess-player in Christendom may be little more than the best player of chess; but proficiency in whist implies capacity for success in all these more important undertakings where mind struggles with mind.”
—Edgar Allan Poe (1809–1845)
“The existence of good bad literature—the fact that one can be amused or excited or even moved by a book that one’s intellect simply refuses to take seriously—is a reminder that art is not the same thing as cerebration.”
—George Orwell (1903–1950)