Once I explained why I needed to know, she was really forthcoming.
“That's what you're here for. Didn't your aunt tell you? She wants you to follow Wilbert Cream and Phyllis about everywhere and see that he doesn't get a chance of proposing.” “You mean that I'm to be a sort of private eye or shamus, tailing them up? I don't like it,” I said dubiously.
Then the following are equivalent: 1) For all high-enough 𝜆, there exists 𝜅<𝜆 such that there is a good 𝜆-frame on the class of 𝜅-saturated models in K_𝜆. 2) For all high-enough 𝜆, K has a unique limit model of cardinality 𝜆. 3) For all high-enough 𝜆, K has a superlimit model of cardinality 𝜆. 4) For all high-enough 𝜆, the union of a chain of 𝜆-saturated models is 𝜆-saturated. 5) There exists 𝜃 such that for all high-enough 𝜆, K is (𝜆,𝜃)-solvable..
Given the degree of fear and loathing inspired by the very thought of a fat body in America today, it is important to emphasize that all of the medical information in the counterfactual world I have just sketched is itself quite factual.
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