# Joint Laver diamonds

## Miha Habič

### The CUNY Graduate Center

Say that a collection of Laver functions is jointly Laver if the functions can guess their targets simultaneously using just a single elementary embedding between them. In this talk we shall examine the notion of jointness in the simplest case of measurable cardinals, giving both equiconsistency results for the existence of large jointly Laver families and separating the existence of small such families from large ones. We shall also comment on how these results transfer to larger large cardinals, such as supercompact and strong cardinals, and, perhaps, how the notion of jointness may be interpreted for guessing principles not connected with large cardinals.

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.