# Topic Archive: joint diamond sequence

Set theory seminarFriday, May 15, 201510:00 amGC 6417

# Constructing joint diamonds from a single diamond

A joint diamond sequence on a cardinal $\kappa$ is a collection of $\diamondsuit_\kappa$ sequences which coheres in the sense that any collection of subsets of $\kappa$ may be guessed on stationary sets in some normal uniform filter on $\kappa$. This is the direct translation of joint Laver diamonds to smaller $\kappa$ which have no suitable elementary embeddings. In this talk I will show that, as opposed to the large cardinal case, joint diamond sequences simply exists whenever $\diamondsuit_\kappa$ holds.