School of Mathematics

Does Infinite Cardinal Arithmetic Resemble Number Theory?

Menachem Kojman
Ben-Gurion University of the Negev; Member, School of Mathematics
February 28, 2011

I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinite cardinal arithmetic and turned out to have applications in other fields.

This modern phase of the theory is marked by absolute theorems and rigid asymptotic structure, in contrast to the era following P. Cohen's discovery of forcing in 1963, during which infinite cardinal arithmetic was almost entirely composed of independence results.