<s>
In	O
mathematical	O
set	O
theory	O
,	O
an	O
ω-Jónsson	O
function	O
for	O
a	O
set	O
x	O
of	O
ordinals	B-Language
is	O
a	O
function	O
with	O
the	O
property	O
that	O
,	O
for	O
any	O
subset	O
y	O
of	O
x	O
with	O
the	O
same	O
cardinality	B-Application
as	O
x	O
,	O
the	O
restriction	O
of	O
to	O
is	O
surjective	B-Algorithm
on	O
.	O
</s>
<s>
Jónsson	B-Algorithm
functions	I-Algorithm
are	O
named	O
for	O
Bjarni	O
Jónsson	O
.	O
</s>
<s>
showed	O
that	O
for	O
every	O
ordinal	B-Language
λ	O
there	O
is	O
an	O
ω-Jónsson	O
function	O
for	O
λ	O
.	O
</s>
<s>
Kunen	O
's	O
proof	O
of	O
Kunen	O
's	O
inconsistency	O
theorem	O
uses	O
a	O
Jónsson	B-Algorithm
function	I-Algorithm
for	O
cardinals	O
λ	O
such	O
that	O
2λ	O
=	O
λℵ0	O
,	O
and	O
Kunen	O
observed	O
that	O
for	O
this	O
special	O
case	O
there	O
is	O
a	O
simpler	O
proof	O
of	O
the	O
existence	O
of	O
Jónsson	B-Algorithm
functions	I-Algorithm
.	O
</s>
<s>
The	O
existence	O
of	O
Jónsson	B-Algorithm
functions	I-Algorithm
shows	O
that	O
for	O
any	O
cardinal	O
there	O
is	O
an	O
algebra	O
with	O
an	O
infinitary	O
operation	O
that	O
has	O
no	O
proper	O
subalgebras	O
of	O
the	O
same	O
cardinality	B-Application
.	O
</s>
<s>
In	O
particular	O
if	O
infinitary	O
operations	O
are	O
allowed	O
then	O
an	O
analogue	O
of	O
Jónsson	O
algebras	O
exists	O
in	O
any	O
cardinality	B-Application
,	O
so	O
there	O
are	O
no	O
infinitary	O
analogues	O
of	O
Jónsson	O
cardinals	O
.	O
</s>
