最終更新日：2024/08/03
(mathematical logic) A theorem stating that, if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The result implies that first-order theories are unable to control the cardinality of their infinite models, and that no first-order theory with an infinite model can have a unique model up to isomorphism.
正解を見る
Löwenheim-Skolem theorem
編集履歴（0）
元となった辞書の項目
Löwenheim-Skolem theorem
name
(mathematical
logic)
A
theorem
stating
that,
if
a
countable
first-order
theory
has
an
infinite
model,
then
for
every
infinite
cardinal
number
κ
it
has
a
model
of
size
κ.
The
result
implies
that
first-order
theories
are
unable
to
control
the
cardinality
of
their
infinite
models,
and
that
no
first-order
theory
with
an
infinite
model
can
have
a
unique
model
up
to
isomorphism.
意味（1）
(mathematical
logic)
A
theorem
stating
that,
if
a
countable
first-order
theory
has
an
infinite
model,
then
for
every
infinite
cardinal
number
κ
it
has
a
model
of
size
κ.
The
result
implies
that
first-order
theories
are
unable
to
control
the
cardinality
of
their
infinite
models,
and
that
no
first-order
theory
with
an
infinite
model
can
have
a
unique
model
up
to
isomorphism.
