n. (Logic) 1. any of the sequence of quantifiers, (∃_nx), read as there are at least n Fs. The first member, (∃₁x), is defined by
(∃₁x) Fx ≡ (∃x) (Fx)
to be equivalent to the existential quantifier, (∃x), and the sequence is defined recursively by
(∃_n+1x) Fx ≡ (∃_nx) (Fx & (∃ y) (Fy & x ≠ y));
that is, there are at least n + 1 Fs is equivalent to there are at least n Fs different from some F.
2. exact numerical quantifier. a restriction on the above, definable in terms of it as
(n x) Fx ≡ (∃_nx) Fx & - (∃_n+1x) Fx.
Alternatively, (1x) Fx can be defined as the unique quantifier,
(∃!x) Fx ≡ (∃x) (Fx & ∀ y) (Fy → x = y)),
whence by recursion
(n+1 x) Fx ≡ (n x) (Fx & (1y) (Fy & x ≠ y)).