# Joint Laver diamonds

## Miha Habič

### The CUNY Graduate Center

A Laver diamond for a given large cardinal $\kappa$ is a function $\ell$, defined on $\kappa$, such that $j(\ell)(\kappa)$ can take any reasonable value, where $j$ is a relevant large cardinal embedding. A sequence of such functions is called jointly Laver or a joint Laver diamond if they can be made to take any given sequence of such values at the same time via a single embedding. In the talk we will consider questions about when such sequences outright exist, when their existence is equiconsistent with and when their existence is consistency-wise strictly stronger than the large cardinal in question.

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.