I think you’re saying Aω+1:=[ΔAω→ΔA0], right? In that case, since A0 embeds into Aω, we’d have Aω+1 embedding into Aω. So not really a step up.
If you want to play ordinal games, you could drop the requirement that agents are computable / Scott-continuous. Then you get the whole ordinal hierarchy. But then we aren’t guaranteed equilibria in games between agents of the same order.
I suppose you could have a hybrid approach: Order ω+1 is allowed to be discontinuous in its order-ω beliefs, but higher orders have to be continuous? Maybe that would get you to ω2.
I think you’re saying Aω+1:=[ΔAω→ΔA0], right? In that case, since A0 embeds into Aω, we’d have Aω+1 embedding into Aω. So not really a step up.
If you want to play ordinal games, you could drop the requirement that agents are computable / Scott-continuous. Then you get the whole ordinal hierarchy. But then we aren’t guaranteed equilibria in games between agents of the same order.
I suppose you could have a hybrid approach: Order ω+1 is allowed to be discontinuous in its order-ω beliefs, but higher orders have to be continuous? Maybe that would get you to ω2.