A, then {a, b}
A and
A
A;
(ii) if a
A and X
A is
0 on A, then
X 
a
A;
(iii) if a
A, X
A is
0 on A, and
xa
y(<x,y>
X), then, for some b
A,
xayb(<x,y>
X).
| This is a file in the archives of the Stanford Encyclopedia of Philosophy. |
(i) if a, bCondition (ii) -- the(ii) if a
(iii) if a
0-separation
scheme -- is a restricted version of Zermelo's axiom of
separation. Condition (iii) -- a similarly weakened version of the
axiom of replacement -- may be called the
0-replacement scheme.
It is quite easy to see that if A is a transitive set such
that <A,
| A> is a model of
ZFC, then A is admissible. More generally,
the result continues to hold when the power set axiom is omitted
from ZFC, so that both
H(
) and
H(1) are
admissible. However, since the latter is uncountable, the Barwise
compactness theorem fails to apply to it.
| John L. Bell jbell@julian.uwo.ca |