<s>
In	O
mathematical	O
logic	O
,	O
the	O
quantifier	B-Algorithm
rank	I-Algorithm
of	O
a	O
formula	O
is	O
the	O
depth	O
of	O
nesting	O
of	O
its	O
quantifiers	B-Language
.	O
</s>
<s>
Notice	O
that	O
the	O
quantifier	B-Algorithm
rank	I-Algorithm
is	O
a	O
property	O
of	O
the	O
formula	O
itself	O
(	O
i.e.	O
</s>
<s>
Thus	O
two	O
logically	O
equivalent	O
formulae	O
can	O
have	O
different	O
quantifier	B-Algorithm
ranks	I-Algorithm
,	O
when	O
they	O
express	O
the	O
same	O
thing	O
in	O
different	O
ways	O
.	O
</s>
<s>
Notice	O
that	O
in	O
Prenex	B-Application
normal	I-Application
form	I-Application
the	O
Quantifier	B-Algorithm
Rank	I-Algorithm
of	O
φ	O
is	O
exactly	O
the	O
number	O
of	O
quantifiers	B-Language
appearing	O
in	O
φ	O
.	O
</s>
<s>
A	O
sentence	O
of	O
quantifier	B-Algorithm
rank	I-Algorithm
2	O
:	O
</s>
<s>
A	O
formula	O
of	O
quantifier	B-Algorithm
rank	I-Algorithm
1	O
:	O
</s>
<s>
A	O
formula	O
of	O
quantifier	B-Algorithm
rank	I-Algorithm
0	O
:	O
</s>
<s>
A	O
sentence	O
in	O
prenex	B-Application
normal	I-Application
form	I-Application
of	O
quantifier	B-Algorithm
rank	I-Algorithm
3	O
:	O
</s>
<s>
A	O
sentence	O
,	O
equivalent	O
to	O
the	O
previous	O
,	O
although	O
of	O
quantifier	B-Algorithm
rank	I-Algorithm
2	O
:	O
</s>
