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:
“Perfect present has no existence in our consciousness. As I said years ago in Erewhon, it lives but upon the sufferance of past and future. We are like men standing on a narrow footbridge over a railway. We can watch the future hurrying like an express train towards us, and then hurrying into the past, but in the narrow strip of present we cannot see it. Strange that that which is the most essential to our consciousness should be exactly that of which we are least definitely conscious.”
—Samuel Butler (1835–1902)
“Children are potentially free and their life directly embodies nothing save potential freedom. Consequently they are not things and cannot be the property either of their parents or others.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“An artist is an artist only because of his exquisite sense of beauty, a sense which shows him intoxicating pleasures, but which at the same time implies and contains an equally exquisite sense of all deformities and all disproportions.”
—Charles Baudelaire (1821–1867)