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It is easy to show that the class is not a null class. Consider the problem, "How can I win the game of tick-tack-toe?" It is well known that I cannot, if I assume (in keeping with the conventions of game theory) that my opponent understands the game perfectly.
My thesis is that the "population problem," as conventionally conceived, is a member of this class.
The population problem cannot be solved in a technical way, any more than can the problem of winning the game of tick-tack-toe.