User blog:KthulhuHimself/Yet another attempt at making an interesting function.

Well, I'm back, and I have a new idea for a function to show everyone. I am aware of how similar it may be to previous functions, but it's interesting nonetheless.

If you see any immediate problems with it, feel free to comment below. I can already imagine that you may have something to say.

Hell, this is pretty much a function identical to what Norminals was meant to be.

Now, consider the language M0. It is, in essence, first order logic.

Now, M1 is in essence first order logic, but with an added symbol that allows it to predicate over the order of logic it is using. In essence, think of it as ath order logic, where a can be any variable defined within a previously established bth order logical expression. Let's use the symbol | for that. To clarify this, let's imagine the following, a pseudo-well-defined expression: "The largest number smaller than any finite number definable within |100|th order logic using 10^100 symbols or less.".

Simple enough, right? Noticed how we called our language M1? Well, let's consider that "1" to be an order of its own. Now, let's let a new language, M1', use that "1" to describe orders. Notice what we have here? Well, let's skip a few steps and consider the following: Some other language, M2, can define orders using a system, within expressions themselves, that by listing collections of other symbols (or new symbols representing specific full expressions that use any other symbols), defines the order in question as the order predicating over all orders definable within the language defined by collection in question. The syntax for this would be something like Q[a,b,c,d,(acb),...] (Q being the order defined, a,b,c,... being the collection of symbols/expressions) Of course, there are many possibilities for ill-defined expressions in such a language (such as including all the symbols in M2 without some sort of limitation), but they don't interest us.

Now, as you can see, we've got a new variable in question. That being, the a in Ma. But before I get into that-

I'll just publish this blog post, since I've got to go.