 Second, he rejected the idea that there must even be a sphere of closest p-worlds. There might, he thought, be closer and closer p-worlds without limit. He called the assumption that there was a sphere of closest worlds the “Limit Assumption”, and noted that we could do without it. The new truth conditions are that p □→ q is true at w if and only if there is a p ∧ q-world closer to w than any p ∧ ¬q-world, or that there is no p world.