20
Why we care: 3
Extensions of FO:
LFP, IFP, PFP, TC, you-name-it,
All are expressible in
infinitary
FO, L
1
,
w
:
Allowed to take infinite conjuctions/disjunctions:
Η
i
2
I
f
i
or
Ζ
i
2
I
f
i
[why ?]
But L
1
,
w
is boring
All are expressible in
[
k
Έ
0
L
k
1
,
w
= L
w
1
,
w