Hypergendered Logic Source
Hypergendered Logic — Page 188
Hyperomega is an HGL-specific developmental boundary chosen so that the local ordinal substage domain
below the boundary has cardinality
:
ℵω
{α: α < Ω𝐻}
|
| = ℵω.
This formalizes the intended statement that there are an
amount of ordinal developmental positions in the
ℵω
local minor-hypercategory progression before the Hyperomega boundary is completed.
A mathematical clarification is important.
is a cardinal, not itself the claim “the greatest ordinal
ℵω
mathematics can express.” Mathematics has ordinals vastly beyond it and has no largest expressible ordinal
in the naive sense. HGL therefore does not identify Hyperomega with a largest mathematical ordinal.
Hyperomega is a deliberately chosen biological-hypercategorical threshold whose initial segment has the
intended enormous cardinality.
If one wants a standard set-theoretic representative, one can choose
to be an initial ordinal of cardinality
Ω𝐻
. HGL is not committed to any stronger set-theoretic claim than the cardinality and ordering properties
ℵω
explicitly stated here.
184. Hyperomega saturation and strict category-lift transitions
SF^Omega_H != HF1; rather, Completed(SF-axis) ->_SIH HF1.
SM^Omega_H != HM1; rather, Completed(SM-axis) ->_SIH HM1.
HF-dimensional saturation != UF1; UF1 is SIH_dim(HF-domain) AND SIH_dim(NOT HM-domain).
HM-dimensional saturation != UM1; UM1 is the exact mirror.
UF-dimensional saturation != AF1; AF1 is SIH_dim(UF-domain) AND SIH_dim(NOT UM-domain).
UM-dimensional saturation != AM1; AM1 is the exact mirror.
The inequality/nonidentity is essential. If the completed source domain were identical to the state that
superinherits it, the definition could create constitutive selfinheritance. HGL therefore adopts Strict
Category-Lift Nonidentity: a category seed is built from the completed lower domain but is not that
lower-domain terminal object.
The transition is analogous not to one instant having two names, but to a new coordinate system being
constructed from a fully completed lower coordinate space. The source remains recoverable through SIH
provenance; it is not identified with the target.
185. Category membership is binary; ordinal advancement is not category
percentage
This is one of the most important rules in the revision.
Suprafemale membership is categorical:
𝑆𝐹𝑎, 𝑡
(
) ∈{0, 1}.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:188.