I don’t think my definition is … inconsistent with the sense used in decision theory.
You defined decision as a mathematical undefinable experience and suggested that it cannot be subject to proofs. That isn’t even remotely compatible with the sense used in decision theory.
It is compatible with it as an addition to it; the mathematics of decision theory does not have decisions happening at particular moments in time, but it consistent with decision theory to recognize that in real life, decisions do happen at particular moments.
You defined decision as a mathematical undefinable experience and suggested that it cannot be subject to proofs. That isn’t even remotely compatible with the sense used in decision theory.
It is compatible with it as an addition to it; the mathematics of decision theory does not have decisions happening at particular moments in time, but it consistent with decision theory to recognize that in real life, decisions do happen at particular moments.