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**Cardinal Spectra**

**Mirna Dzamonja**

*University of East Anglia*
We define the notion of a cardinal spectrum, as a class-valued cardinal
function. After a discussion of various contexts in which such functions
are studied, we take up the example of the universality spectrum and explain
its relevance to certain problems in set theory and model theory. Through
this example, we explain what sort of problems one may face when trying
to calculate such spectra, mostly having to do with difficulties in providing
independence results in set theory at certain sort of cardinals (successors
of singulars). We then describe some results (including a joint result
by S. Shelah and the speaker) which resolve some of the issues arising
in this context, and give directions of present research (joint with C.
Morgan).