Last Updated：2025/11/28
(mathematics) The residual operation of a Heyting algebra when considered as a residuated lattice whose monoid operation is the meet operation. Equivalently, the relative pseudo-complement of a with respect to b is the supremum of the set of all z such that z∧a⩽b, where ∧ denotes the meet operation of the given Heyting algebra.
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relative pseudo-complement
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Source Word
relative pseudo-complement
Noun
(mathematics)
The
residual
operation
of
a
Heyting
algebra
when
considered
as
a
residuated
lattice
whose
monoid
operation
is
the
meet
operation.
Equivalently,
the
relative
pseudo-complement
of
a
with
respect
to
b
is
the
supremum
of
the
set
of
all
z
such
that
z∧a⩽b,
where
∧
denotes
the
meet
operation
of
the
given
Heyting
algebra.
Japanese Meaning
Heyting代数において、meet（∧）演算を単位元とするレジデュエーテッド格子として考えた場合の残余操作を指す。すなわち、bに関するaの相対擬似補元は、z ∧ a ≤ bとなるすべてのzの中での上限である。
Sense（1）
(mathematics)
The
residual
operation
of
a
Heyting
algebra
when
considered
as
a
residuated
lattice
whose
monoid
operation
is
the
meet
operation.
Equivalently,
the
relative
pseudo-complement
of
a
with
respect
to
b
is
the
supremum
of
the
set
of
all
z
such
that
z∧a⩽b,
where
∧
denotes
the
meet
operation
of
the
given
Heyting
algebra.
（ plural ）
