|Time:|| 12 - 1:20 p.m.
Baker Hall 150
|Speaker:|| Andreas Liu
Department of Mathematics
Hebrew University of Jerusalem
Cardinal arithmetic since Silver
A famous theorem of Silver, published in 1974, states that if the
generalized continuum hypothesis holds below a singular cardinal of
uncountable cofinality, then it holds also at that cardinal. This result
surprised almost everyone, and raised hopes that cardinal arithmetic might
contain a substantial "core" theory immune to forcing.
Since then, Shelah's pcf theory has justified these hopes to a great extent; along the way, it has changed the language of cardinal arithmetic by focusing attention on relatively concrete objects whose properties are often fixed by the ZFC axioms. In particular, it has proven fruitful to study the "pseudopower" function in place of the classical power function on singular cardinals.
The talk will introduce pseudopowers, survey some results and questions
connected with them, and describe how methods from pcf theory can be used
to extend Silver's theorem in several directions.