Here, in the Von Neumann universe, lived an ordinary man named James. He was a professor who studied the oddities of the universe he lived in, and he was also a mathematician who carefully studied cardinality.
On a bright morning, James' son, Iscaroth, left the house before going on a picnic with his family. On that Saturday, the day of the picnic, James and his wife, Oliver, were packing their things for a picnic in the mountains.
Iscaroth wandered off and took a few steps before he found a large puddle of water. He stared at the puddle, feeling as if something was calling him from within.
As he tried to move away from the puddle, he suddenly lost his balance and fell into it. Unexpectedly, the puddle was as deep as the ocean, with no bottom in sight. He was about to pass out from lack of oxygen, but just before he lost consciousness, infinite symbols appeared before his eyes, such as the symbols א, β, κ, λ, and others.
When he woke up, he was in a cave tunnel with only one way forward. He held his head with his hands because of the headache caused by what had happened. He crawled through the tunnel, muttering a little about the misfortune that had befallen him. On the other side, James and Oliver, who were putting their belongings in the trunk of the car, realized that their only child was missing. James, panicking, tried to leave and look for Iscaroth, but suddenly his head began to buzz—he heard voices that didn't make sense—making him feel hypnotized. When he opened his eyes again, he saw Oliver like a horny animal. For some reason, Oliver suddenly took off all his clothes—then he teased James into doing sexual things. Driven by his reproductive instincts, James couldn't resist and ended up carrying Oliver upstairs—to his room—to have sex.
Iscaroth, who had crawled three kilometers through the tunnel, finally found a widening in the tunnel—wide enough for him to stand. "Finally, I can stand after crawling for so long. My back hurts so much."
When he tried to point the way with his finger, fire came out of his finger—he was shocked and tried it again and again, and finally he realized, "What is this, do I have the power to control fire? It seems so." Unfortunately, the six-year-old boy was trapped in this tunnel.
About twelve years later—James and Oliver were still trying to find their son, Iscaroth.
Iscaroth himself was now an eighteen-year-old teenager. James put up many posters about his missing son, but after twelve years, none of them yielded any results, not even a small clue. Meanwhile, Iscaroth, who was in the tunnel, gained several benefits by continuing to move forward, such as special abilities that ordinary humans couldn't possess, or intellectual intelligence that surpassed even the smartest people, and he received some clothes and food that came from who knows where.
Iscaroth was still walking—dressed like a doctor during the Black Death. He didn't understand why he liked those clothes, but he didn't think about it too much. Just as he was about to give up and kill himself, he saw a light. He immediately ran toward the source of the light. When he came out, he found a bright world, with high, beautiful mountains and vast expanses of green grass, like paradise. Iscaroth was mesmerized by the beauty of this world, unaware of anything else.
James was suddenly contacted by his friend, who had found all the papers he believed to be clues about Iscaroth's whereabouts. James went to the location Jonathan had sent him. When he arrived, he and Jonathan found an old table inside an abandoned house. He saw a computer there, as well as many terrifying papers. This was Professor O'ok's house—as James and Jonathan read the papers, they both discovered a proposal for a portal that could only be opened by a chosen person. Professor O'ok experienced an illusion that he believed to be a clue from a supreme entity in this world. James and Jonathan opened the proposal more carefully.
"When the Computer has made its choice,
Its choice will be tested
To determine its suitability
Against all forms of darkness,
To nurture creatures so they will not fear.
He is Is******."
"What's the rest of this writing?" asked Jonathan.
At that moment, the old computer turned on, showing the frightened face of Professor O'ok, saying incomprehensible things, saying "our end is near! Quickly find the child, he has a sun mark on the back of his neck!" At that moment, the computer suddenly turned off. James suddenly panicked and remembered that his child had the same birthmark as the one mentioned by the professor. He opened another page titled "Our Universe."
"On March 27, I researched the farthest star from the solar system.
I don't know why I had a feeling that this was not a good thing.
I continued my research,
driven by curiosity.
I tried using the cardinality theory.
Finally, I found it.
Our universe has a Berkeley Cardinal structure.
A cardinal δ is ζ-proto Berkeley, for some ordinal ζ < δ, iff
for all transitive M with δ ∈ M there is an elementary embedding j : M → M
with ζ < crit j < δ. A cardinal δ is Berkeley iff it is ζ-proto Berkeley for all ζ < δ.
A cardinal δ is ζ-proto Berkeley iff for all transitive M with δ ∈
M and all b ∈ M there is an elementary embedding j : M → M with ζ < crit j < δ
and j(b) = b.
For any fixed ordinal ζ, the least ζ-proto Berkeley cardinal,
if it exists, is also a Berkeley cardinal.
For our purposes, we will also be interested in a somewhat weakened version of
Berkeley cardinals. We will simply restrict the definitions to transitive sets M of
the form Vλ for some λ.
A cardinal δ is ζ-proto rank-Berkeley, for some ordinal ζ < δ, iff
for all λ > δ there is an elementary embedding j : Vλ → Vλ with ζ < crit j < δ and
j(δ) = δ. A cardinal δ is rank-Berkeley iff it is ζ-proto rank-Berkeley for all ζ < δ.
Let Eλ denote the set of all nontrivial elementary embeddings j : Vλ → Vλ
and let Eδλ = {j ∈ Eλ | crit j < δ and j(δ) = δ}. We want to have an analogue of which will allow us to impose the extra condition of fixing an arbitraryordinal α ∈ Vλ on j : Vλ → Vλ. For this, we first need to define an operation from Eδ λ × Eδλ to Eδ λ.
If λ is a limit ordinal, then for any j, k : Vλ → Vλ define theoperation j[k], the application of j to k, by setting j[k] = Sγ<λ j(k|Vγ).
f λ is a limit and j, k ∈ Eδλ, then j[k] is also in Eδλ. Moreover,crit j[k] = j(crit k).Now, for limit λ and j ∈ Eδλ, define j0 = j and jn+1 = j[jn]. By induction
and the previous lemma, each jn is in Eδλ.
For limit λ, any j ∈ Eδλ, and each α ∈ Vλ there isn such that jm(α) = α for all m ≥ n.
For any ordinal ζ, the least ζ-proto rank-Berkeley cardinal, if it
exists, is also a rank-Berkeley cardinal
Proof. Let δ be the least ζ-proto rank-Berkeley cardinal and suppose it is not rank-Berkeley. Fix α ∈ (ζ, δ) and λ > δ such that ∀j ∈ Eδ
λ(crit j ≤ α). We will showthat α must be a ζ-proto rank-Berkeley, contradicting the choice of δ.
Let µ > α be arbitrary and let ν be an ordinal above max{µ, λ}. By ζ-proto
rank-Berkeleyness of δ, fix a j ∈ Eδνsuch that crit j > ζ. there is n
such that jn fixes α, λ, and µ, and moreover, crit jn > ζ. Now, jn|Vλ ∈ Eδ
λ, hencecrit jn ≤ α. But also jn(α) = α, so in fact crit jn < α. Finally, since jn fixes µ, wecan restrict jn to Vµ so that jn|Vµ witnesses ζ-proto rank-Berkeleyness of α at thearbitrary ordinal µ."
After reading the sheet, James and Jonathan still did not understand what it had to do with His Son.
Meanwhile, unbeknownst to Iscaroth, the cosmic beings had already seen Iscaroth passing through the tunnel. The tunnel was not bound by the flow of time, which made Iscaroth considered not an ordinary human by the Cosmic Beings because he could walk and move without any irregularities.