<s>
In	O
mathematical	O
logic	O
,	O
a	O
Lindström	B-Algorithm
quantifier	I-Algorithm
is	O
a	O
generalized	O
polyadic	O
quantifier	O
.	O
</s>
<s>
Lindström	B-Algorithm
quantifiers	I-Algorithm
generalize	O
first-order	O
quantifiers	O
,	O
such	O
as	O
the	O
existential	B-Algorithm
quantifier	I-Algorithm
,	O
the	O
universal	O
quantifier	O
,	O
and	O
the	O
counting	B-Algorithm
quantifiers	I-Algorithm
.	O
</s>
<s>
They	O
were	O
later	O
studied	O
for	O
their	O
applications	O
in	O
logic	B-Application
in	I-Application
computer	I-Application
science	I-Application
and	O
database	B-Language
query	I-Language
languages	I-Language
.	O
</s>
<s>
For	O
a	O
concrete	O
example	O
,	O
take	O
the	O
universal	O
and	O
existential	B-Algorithm
quantifiers	I-Algorithm
and	O
,	O
respectively	O
.	O
</s>
<s>
A	O
Lindström	B-Algorithm
quantifier	I-Algorithm
is	O
a	O
polyadic	O
generalized	O
quantifier	O
,	O
so	O
instead	O
being	O
a	O
relation	O
between	O
subsets	O
of	O
the	O
domain	O
,	O
it	O
is	O
a	O
relation	O
between	O
relations	O
defined	O
on	O
the	O
domain	O
.	O
</s>
<s>
Lindström	B-Algorithm
quantifiers	I-Algorithm
are	O
classified	O
according	O
to	O
the	O
number	O
structure	O
of	O
their	O
parameters	O
.	O
</s>
<s>
An	O
example	O
of	O
a	O
type	O
(	O
4	O
)	O
quantifier	O
is	O
the	O
Henkin	B-Algorithm
quantifier	I-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
adding	O
a	O
"	O
there	B-Algorithm
exist	I-Algorithm
finitely	O
many	O
"	O
quantifier	O
results	O
in	O
a	O
loss	O
of	O
compactness	O
,	O
whereas	O
adding	O
a	O
"	O
there	B-Algorithm
exist	I-Algorithm
uncountably	O
many	O
"	O
quantifier	O
to	O
first-order	O
logic	O
results	O
in	O
a	O
logic	O
no	O
longer	O
satisfying	O
the	O
Löwenheim	O
–	O
Skolem	O
theorem	O
.	O
</s>
