No seminar today, Monday, October 27 (university closed).

Speaker:
Santi Spadaro, University of Sao Paulo.Time and Date: Monday October 20 at 2PM. Room: 266A. Abstract: "Sparse families are a set-theoretic tool that provides the combinatorial skeleton for many seemingly unrelated problems from various areas of mathematics. For example, Kojman, Milovich and I used them to find bounds for the cardinality of bounded subsets in certain topological bases and Blass used them to find bounds for the cardinality of the divisible part of certain quotient groups. A family of countable sets of a given cardinal is sparse if every uncountable subfamily has uncountable union. Good PCF scales yield large sparse families, while variants of Chang Conjecture can be used to destroy them. In this first lecture we will focus on how to construct large sparse families." ## CARDINAL ARITHMETIC AND REFLECTION THEOREMS FOR tHE LINDELOF DEGREE - NOTES BY ALBERTO LEVI10/18/2014 Here are the notes prepared by Alberto Levi regarding his series of seminar lectures (29/09-12/10).
Date and time: Monday, October 13 at 2PM
Room: 266A. Speaker: Alberto Levi, University of Sao Paulo.Abstract: "We present some reflection results for the Lindelöf degree of a topological space X, that is the minimum cardinal k such that every open cover of X has a subcover of cardinality k. After a short review of some facts about exponentiation of singular cardinals, we apply some results of PCF Theory to the problem of reflection. Then, we examine some hypotheses of PCF Theory, like SSH (Shelah's Strong Hypothesis) and SWH (Shelah's Weak Hypothesis), their status in ZFC, and some consequences. Finally, we present some open questions relative to this matter."Date and time: Monday, September 29 at 2PM
Room: 266A. Speaker: Alberto Levi, University of Sao Paulo.Abstract: "We present some reflection results for the Lindelöf degree of a topological space X, that is the minimum cardinal k such that every open cover of X has a subcover of cardinality k. After a short review of some facts about exponentiation of singular cardinals, we apply some results of PCF Theory to the problem of reflection. Then, we examine some hypotheses of PCF Theory, like SSH (Shelah's Strong Hypothesis) and SWH (Shelah's Weak Hypothesis), their status in ZFC, and some consequences. Finally, we present some open questions relative to this matter.". |
## ARCOIRISThis is the abstract blog of our PCF theory seminar. ## Archives
January 2015
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