What is "w", the permission to make modifications?

Question

As per chapter 9 of the yellow paper:

However, I find it vaguely defined.

1. Who gives this permission? Is it dependent on each machine or is there an objective algo to follow?
2. What is the type of "w"? In the paper, it seems to always take the value of an opcode (e.g. REVERT), but I'm not fully sure.

I know about this answer but it simply pasted snapshots from the yellow paper and it's not descriptive enough + I'm not sure it's correct, it seems "w" is not a boolean.

Answer 1

The answer was down the rabbit hole:

Therefore, the answers are:

1. No, if a node uses a non-malicious Ethereum client, there's no subjectivity involved. The permission is given by the specified operands.
2. The type is an operand or an instruction, like ADD, PUSH or STOP. The full table of instructions is specified in Appendix H.

Note: what I find a bit unwieldy about the yellow paper is that it uses many symbols and concepts without super-scripting a reference to them. You just have to go through and hope that it will be defined in the next page or in some Appendix.