# Constructing joint diamonds from a single diamond

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

# Constructing joint diamonds from a single diamond

### The CUNY Graduate Center

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.

Miha Habič is a graduate student at the CUNY GC. He got his Masters Degree in Mathematics at the University of Ljubljana, Slovenia. His interests lie in the area of infinitary computability, forcing and large cardinals.

Posted by on May 11th, 2015