The schemafield contains not only infinitely many such ideas as "the empty set" or "the complete set", but also all the means of constructing them, anything equivalent to them, any abstractions of them, and any greater or lesser operations that can or cannot be applied to them in any way.
While it vaguely resembles a conventional cosmological structure more than it does a single function like a Prism Gate, comparing the schemafield to -verses of more concrete size or contents is not entirely proper, since even making statements about what similarities it has to lesser -verses counts only as a generalization, and neglects its full extent.
For the sake of simplicity in understanding, it can be useful to see the schemafield as a means of generalizing over the basic processes of abstraction that allow for certain hierarchies and tools to work. While one region of the schemafield uses the conventional Prism-Gate-like functionality of taking an input and viewing it as a degenerate case of something else, other regions handle input entirely differently.
Naturally, since generalization forms only a part of the schemafield, no matter how many times one attempts to apply it, one finds the exact same problem every time - there will always be regions that generalization cannot reach and that only more powerful operations (which also exist within the schemafield) can.
Similarly, there are other "approaches" up the schemafield using functions that it itself contains, none of which can apply to its full extent. Completing a thorough definition of the schemafield using only one of these is therefore effectively impossible.
Another approach would be to define information first, and then have the Schemafield contain that information.
- x is formal means x can be represented as a string in a formal language.
- x is information means x is formal or can be obtained from references from information. A reference to a cosmology x is a statement which x satisfies, such as "x is red".
One may doubt if this is sufficient to describe the Schemafield. However, you can easily demonstrate that operations such as generalization and abstraction are within this interpretation, as you can write down "x is generalization" or "x is abstraction" within our universe. However this assumes the universe is a formal structure, which seems likely, given how the universe can be demonstrated to follow mathematical law, and how elementary particles can be described as solutions to equations.
Below the schemafield exist domains and regions where only particular groups of information arrangements and concept comparisons apply. One such area, for example, is the area in which general and degenerate cases exist in the way in which we are familiar, and in which Prism Gates operate normally. Others may share this property, of course, but some ignore it altogether.
Past the schemafield, operations on information break down entirely, nothing can be compared, and no organizational pattern applies.