There is an inconsistency in Gödel's axioms yet I use the proof for my model of the Holy Trinity in my book "Seven Eyes Open" (Fourth Edition). The axiom of virtue added to Gödels axioms adequately dismisses the empty essence lemma as sets of positive properties have principal elements in GF(8) and form separate ultrafitlers partitioning the set of all predicates on a Godlike being, as in the model. The treatment is lengthy, but the metaphysics only requires a proof or two.

I begin to lay ground for asserting that the model of the Trinity holds firm with Gödel's original axioms, none should be altered or discarded; only the axiom of virtue requires adding to them. Gödel's asumptions may have been invalid but his axioms are consistent, as there is a model that holds firm with the "empty essence lemma".

Notes On The Model
I make a few introductory notes on the model of GF(8) in the book "Seven Eyes Open" (Fourth Edition).

Objections Enumerated
I list some objections to the empty essence lemma, in that they will have consequences for the model; I will include more metaphysics in the pages to follow.

Ω Is Partitioned
I simply include a proof that the set of all positive properties may be partitioned without contradicting Gödel's axioms or definition of the positive and of the "Godlike".

The Empty Essence Is Incompossible
I supply another proof which, by elimination reduces the empty essence to the empty set: it becomes incompossible.

The Problem Of Zero
There is one element remaining in the set of Ω besides the seven separate Godlike essences in GF(8); the zero. I take a look at that here as it is actually never equal to the empty essence.

Proof Of Gödel's Argument
A simple summing up; not to be found too confusing I hope, but I give it here.

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