User blog comment:Ytosk/Trying to define Bowers' K(n) systems/@comment-35470197-20191031094256/@comment-38817512-20200206233246

I'm sorry i haven't been here for a few months. I'll try to be as active as possible in the future.

> r is not canonically determined by the system

I don't see why it shouldn't be. Set membership is a relation in set theory, just like r is in that axiomatic system. Set membership is defined by the axioms of its axiomatic system, just like r. There is no difference between r and set membership, other than the definitions. So why is r treated differently?

> you need to specify the way to make a system to include arithmetic.

That's something i forgot in the definition, so thank you for mentioning it. I think that should only need a well-ordered set and the relation that well-orders it. So let's define max(X) to be the greatest element of X, which is a set of ordinals, let's define Def(x) to be the definability of x, and if x is a set, the formula used to define x can use the set membership relation. MK(n,m)=max({|L| | א‎0>|L|∧∃o∃S∃r((o is a K(m) system)∧(r well-orders S)∧∀x∈S((the axioms of o can prove the existence of x)∧(Def(S)+Def(r)+Def(x)≤n⇒∀y∈S(r(y,x)⇒y∈L)))∧∀y∈L∃x∈S((the axioms of o can prove the existence of x)∧Def(S)+Def(r)+Def(x)≤n∧r(y,x)))})

There are still some obvious problems with what i wrote, but it shouldn't be too hard to fix. If you read the end of my comment, you will know why i'm not fixing it.

> Which word?

I'm sorry if i was rude, i have no idea why i said it like that. I think i meant the word oracle. Now i realize that it's a normal english word and google translator told me what it means, but i think that's far from the meaning in mathematics, which i don't know.

> No, it is not kind of an identity. It is a (non-unique) predicate which evaluates whether a given formula is true or not.

That sounds like a contradiction to me, but as you said, i shouldn't doubt someone if i don't understand what they said. Truth predicate seems to be as difficult to understand as the "Exceptionally simple theory of everything", because not only do i not understand it, i don't even know which part i don't understand. So i can't point out what exactly i don't understand.

This whole thing took me 1.5 hours to write and then when i tried to post it, it just got deleted because i was on the page too long. It said "Refresh page and try again", so here i am, trying it again after midnight. Someone should fix that. I'm just saying this to calm myself down, while i try to remember what i said before.