Last Updated：2025/12/07
(set theory) The original form of forcing, starting with a model M of set theory in which the axiom of constructibility, V = L, holds, and then building up a larger model M[G] of Zermelo-Fraenkel set theory by adding a generic subset G of a partially ordered set to M, imitating Kurt Gödel's constructible hierarchy.
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ramified forcing
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Source Word
ramified forcing
Noun
uncountable
(set
theory)
The
original
form
of
forcing,
starting
with
a
model
M
of
set
theory
in
which
the
axiom
of
constructibility,
V
=
L,
holds,
and
then
building
up
a
larger
model
M[G]
of
Zermelo-Fraenkel
set
theory
by
adding
a
generic
subset
G
of
a
partially
ordered
set
to
M,
imitating
Kurt
Gödel's
constructible
hierarchy.
Japanese Meaning
集合論において、構成可能性公理 (V = L) が成立するモデル M を出発点とし、部分順序集合からの生成的部分集合 G を加えることで、Zermelo-Fraenkel集合論の拡大モデル M[G] を構築する手法。これは、Kurt Gödel の構成階層の考えに触発された、forcing の原初形態を指す。
Sense（1）
(set
theory)
The
original
form
of
forcing,
starting
with
a
model
M
of
set
theory
in
which
the
axiom
of
constructibility,
V
=
L,
holds,
and
then
building
up
a
larger
model
M[G]
of
Zermelo-Fraenkel
set
theory
by
adding
a
generic
subset
G
of
a
partially
ordered
set
to
M,
imitating
Kurt
Gödel's
constructible
hierarchy.
