mocha:

Kate stood by the window, looking out drearily at the matinal sunlight.

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..

John Henry collects stamps.