Proposition 16.2.
Assuming that:
p
∈
S
n
M
(
A
)
.
Then
the following are equivalent:
(i)
p
is
isolated
(ii)
{
p
}
=
[
φ
(
z
)
]
for some
L
A
-formula
φ
(
x
¯
)
. In this case we say
φ
(
x
¯
)
isolates
p
.
(iii)
There is an
L
A
-formula
φ
(
x
¯
)
∈
p
such that for any
ψ
(
x
¯
)
∈
p
,
T
h
A
(
M
)
⊨
∀
x
(
φ
(
x
¯
)
→
ψ
(
x
¯
)
)
.