The fact that U is an ultrafilter ( and not just a filter ) is used in the negation clause, and the axiom of choice is needed at the existential quantifier step.
32.
The above two rules for universal and existential quantifiers are correct, and so are the propositional rules : if a set of formulae generates a closed tableau, this set is unsatisfiable.
33.
In fact, it is sufficient here to show that any sentence with only existential quantifiers have the same truth value in " B " and " C ".
34.
I have devised a procedure for testing a single existential quantifier for a variable that is only used in the first degree, but the procedure can't handle anything more complicated.
35.
The converse is true as well : Suppose \ varphi ( n ) is a formula in \ Sigma ^ 0 _ 2 with k 1 existential quantifiers followed by k 2 universal quantifiers.
36.
Now Suppose \ varphi ( n ) is a formula in \ Sigma ^ 0 _ { p + 2 } with k 1 existential quantifiers followed by k 2 universal quantifiers etc ..
37.
Quine argued that the only ontologically committing expressions are variables bound by a first-order existential quantifier, and natural language expressions which were formalized using variables bound by first-order existential quantifiers.
38.
Quine argued that the only ontologically committing expressions are variables bound by a first-order existential quantifier, and natural language expressions which were formalized using variables bound by first-order existential quantifiers.
39.
In particular, a formula with a leading existential quantifier like \ exists x . \ delta ( x ) generates its Skolemization \ delta ( c ), where c is a new constant symbol.
40.
We define the "'degree "'of \ phi to be the number of universal quantifier blocks, separated by existential quantifier blocks as shown above, in the prefix of \ phi.
