Notes on Singular Cardinal Combinatorics

Singular Cardinal Combinatorics

From May 1 to May 6, 2004 24 set theorists met at the Banff International Research Station to discuss Singular Cardinal Combinatorics. Descriptions of the contents of their talks will be published in a Proceedings that will appear in the Notre Dame Journal of Symbolic Logic. During the workshop, several important new results were announced and explained, and there were problem sessions held (so...

Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics

The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing axioms and then translate the results so obtai...

Singular Combinatorics ∗

Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit probability distributions present in large random structures. “Singularity analysis” reviewed here provides constructive estimates that are applicable in several areas...

Lecture Notes on Algebraic Combinatorics

Singular Cardinal Problem : Shelah

This is an expository paper giving a complete proof of a theorem of Saharon Shelah: If 2n < @! for all n < !, then 2! < @!4 .