Partitioning a cardinal into fat stationary sets, part 1

Seminar
Speaker
Assaf Rinot
Date
29/12/2016 - 12:00 - 10:00Add to Calendar 2016-12-29 10:00:00 2016-12-29 12:00:00 Partitioning a cardinal into fat stationary sets, part 1 A subset F of a regular uncountable cardinal kappa is said to be fat iff for every club C in kappa, and every ordinal alpha<kappa, F\cap C contains a closed copy of alpha+1. By a theorem of H. Friedman from 1974, every stationary subset of w1 is fat. In particular, w1 may be partitioned into w1 many pairwise disjoint fat sets. In this talk, I shall prove that square(kappa) give rise to a partition of kappa into kappa many pairwise disjoint fat sets. In particular, the following are equiconsistent: w2 cannot be partitioned into w2 many pairwise disjoint fat sets; w2 cannot be partitioned into two disjoint fat sets; there exists a weakly compact cardinal.   seminar room אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
seminar room
Abstract

A subset F of a regular uncountable cardinal kappa is said to be fat iff for every club C in kappa, and every ordinal alpha<kappa, F\cap C contains a closed copy of alpha+1.
By a theorem of H. Friedman from 1974, every stationary subset of w1 is fat. In particular, w1 may be partitioned into w1 many pairwise disjoint fat sets.

In this talk, I shall prove that square(kappa) give rise to a partition of kappa into kappa many pairwise disjoint fat sets. In particular, the following are equiconsistent:

  1. w2 cannot be partitioned into w2 many pairwise disjoint fat sets;
  2. w2 cannot be partitioned into two disjoint fat sets;
  3. there exists a weakly compact cardinal.

 

Last Updated Date : 28/10/2019