You use B as a predicate symbol for "belief" I think.  What are some 
properties of B and is there a predicate for knowing/being aware of that 
might lead to a definition for self-awareness?

btw, what is a machine and what types of machines are there?

Is there a generic description for a structure (in the math logic sense) to 
have a belief or to be aware; something like
A |= "I am the structure A"

Finally, on a different note, if there is a structure for which all 
structures can be 1-1 injected into it, does that in itself imply a sort of 
ultimate structure perhaps what Max Tegmark views as the level IV 

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