User blog:KthulhuHimself/Norminals

At last. I'm finally getting to defining this. After all the attempts at IRC, after all my ranting and rambling, I can at last formalize it.

Note
I will use the term "FONT(n)" to define the finalized output of the "norminals" function, with some base value n.

Terms
Well, What are norminals?

For starts, I'll try to explain the concept of "terms", which are crucial to defining norminals.

Informally, a term is a concept used in or to define a language.

I have no single formal definition for terms, yet I can try, so why not?

First, allow any statement (phi) to represent any logical connection between two sets, for example, "the mamber 2 is not an element of the member 5" This logical connection between member 2 and member 5 is a statement, or a formula. The terms used is this formula were: ordinality ("member"), "2", "5", negation ("is not"), and membership ("element of"). This entire logical connection can be called (phi), can't it? We have now defined a new term.

N-tongue
First define a language "N(0)". This will serve as our base language, and is somewhat (very) similar to FOST. It contains all the terms, sets, arguments, classes, etc. used in FOST.

N-chess
In order to reach the next norminal, we first have to play a game, so to speak. For clarity, I will try to simplify the idea (as I myself don't truly know how this will work or where it will lead to).

We first need to state how to form connections between terms, so that the terms can interact.

We start with N(0)-chess, the most simple form of N-chess, and the easiest to define.