While Mu Cang was joking and laughing, the power of perception, which was due to the loss of the narrow abyss, was groping around like a spider minesweeper, and it immediately swept over and covered his whole body.

Buzz!!!

In an instant, the [Wujue Secret Strategy] was activated independently under the stimulation of a strong threat, teleporting Mu Cang out of thin air to the source of this exploratory force - a Tuoshu complex with a large cardinal axiom structure located at the bottom of the Yanyi branch defense line.

in the universe.

He started a new round of "confrontation".

Therefore, with the countless high-level Taoists at all levels falling from their thrones and becoming ants, and the collapse of the infinite number of large cardinal universes and even larger hierarchical structures, Mu Cang's main body, marrow, foundation, and essence

...and so on, it continued to rise all the way up and began to rise crazily and violently.

weak compact base

n1,0-indescribable cardinality

n1,10-indescribable cardinality

n1,100 - indescribable cardinality

…

n2,0-indescribable cardinality

n10,0-indescribable cardinality

n100,0-indescribable cardinality

…

Finally, after going through a series of endless "hits".

Mu Cang finally reached the top of Yanyi Branch's defense line, and stopped at the so-called... [completely indescribable base] level.

This large cardinal number belongs to the ultimate end of the boundless ocean [the entire field of indescribable cardinal numbers].

But even this end is infinitely larger and infinitely larger than the entire indescribable ocean.

The so-called "indescribable", as the name suggests, refers to the indescribable properties of this large cardinality.

The axiomatic definitions and mathematical structures of such large cardinal numbers are very complicated.

So putting aside those complicated information, the indescribable cardinality can be roughly understood as a large cardinality axiom that needs to be established in the domain of second-order arithmetic to be established without contradiction.

As for the so-called several-order arithmetic, it is another extremely complex mathematical concept.

"Sub-concepts" related to this concept include predicates, logic, propositions, etc.

The relationship between them is that [Logic] uses [Predicate] to propose [Propositions], and [Arithmetic] is a special case of these three that have axioms of arithmetic.

In short, you only need to know that first-order arithmetic only refers to natural numbers, which are the quantification of entities [objects], such as 1, 2,500, 10^100, etc.

Second-order arithmetic reference is the attribute of natural numbers, which is the quantification of abstract [properties], such as odd numbers, even numbers, prime numbers, etc.

The third-order arithmetic above these two further quantifies the attributes of the already quantified [properties].

Is it very abstract?

It's very abstract indeed.

So, is this the end of third-order arithmetic?

No, it's not.
Chapter completed!