Downward LS: consistent T in countable signature has a countable model. Upward LS: infinite model ⟹ models of every κ ≥ |T|. Compactness corollary.
Downward LS: consistent T in countable signature has a countable model. Upward LS: infinite model ⟹ models of every κ ≥ |T|. Compactness corollary.