<s>
In	O
first-order	O
logic	O
the	O
empty	B-Algorithm
domain	I-Algorithm
is	O
the	O
empty	O
set	O
having	O
no	O
members	O
.	O
</s>
<s>
Interpretations	O
with	O
an	O
empty	B-Algorithm
domain	I-Algorithm
are	O
shown	O
to	O
be	O
a	O
trivial	O
case	O
by	O
a	O
convention	O
originating	O
at	O
least	O
in	O
1927	O
with	O
Bernays	O
and	O
Schönfinkel	O
(	O
though	O
possibly	O
earlier	O
)	O
but	O
oft-attributed	O
to	O
Quine	O
1951	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
an	O
existential	O
quantification	O
of	O
the	O
open	O
formula	O
is	O
true	O
in	O
a	O
model	O
iff	O
there	O
is	O
some	O
element	O
in	O
the	O
domain	B-Algorithm
(	O
of	O
the	O
model	O
)	O
that	O
satisfies	O
the	O
formula	O
;	O
i.e.	O
</s>
<s>
A	O
universal	O
quantification	O
of	O
an	O
open	O
formula	O
is	O
true	O
in	O
a	O
model	O
iff	O
every	O
element	O
in	O
the	O
domain	B-Algorithm
satisfies	O
that	O
formula	O
.	O
</s>
<s>
Logics	O
whose	O
theorems	O
are	O
valid	O
in	O
every	O
,	O
including	O
the	O
empty	O
,	O
domain	B-Algorithm
were	O
first	O
considered	O
by	O
Jaskowski	O
1934	O
,	O
Mostowski	O
1951	O
,	O
Hailperin	O
1953	O
,	O
Quine	O
1954	O
,	O
Leonard	O
1956	O
,	O
and	O
Hintikka	O
1959	O
.	O
</s>
