<![CDATA[SANTI SPADARO - PCF Abstracts]]>Sat, 30 May 2020 11:09:01 -0700Weebly<![CDATA[A DOWKER SPACE OF CARDINALITY aleph_{omega+1}, II]]>Wed, 14 Jan 2015 12:59:23 GMThttp://www.santispadaro.com/pcf-abstracts/a-dowker-space-of-cardinality-aleph_omega11Speaker: André Ottenbreit, University of Sao Paulo.

Time and Date: Monday, December 1 at 2PM. Room: 266A.

Abstract: "We'll show Kojman and Shelah's construction from a PCF scale of a "small" normal space $X$ such that $X \times I$ is not normal ".]]><![CDATA[A dowker space of cardinality aleph_{omega+1}]]>Wed, 14 Jan 2015 12:56:53 GMThttp://www.santispadaro.com/pcf-abstracts/a-dowker-space-of-cardinality-aleph_omega1Speaker: André Ottenbreit, University of Sao Paulo.

Time and Date: Monday, November 24 at 2PM. Room: 266A.

Abstract: "We'll show Kojman and Shelah's construction from a PCF scale of a "small" normal space $X$ such that $X \times I$ is not normal ".]]><![CDATA[SPARSE FAMILIES AND THEIR APPLICATIONS, III]]>Mon, 17 Nov 2014 12:57:45 GMThttp://www.santispadaro.com/pcf-abstracts/sparse-families-and-their-applications-iiiSpeaker: Santi Spadaro, University of Sao Paulo.

Time and Date: Monday, November 17 at 2PM. Room: 266A.

Abstract: "We'll work out the proof that there is in ZFC an aleph_4-sparse family of countable subsets of aleph_omega having maximal size. "aleph_4-sparse" means that every aleph_4-sized subfamily has uncountable union. The main ingredients are club guessing and PCF scales".]]><![CDATA[SPARSE FAMILIES AND THEIR APPLICATIONS II]]>Thu, 06 Nov 2014 20:41:10 GMThttp://www.santispadaro.com/pcf-abstracts/sparse-families-and-their-applications-iiSpeaker: Santi Spadaro, University of Sao Paulo.

Time and Date: Monday, November 3 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.

In this second lecture we will show how to use Chang's Conjecture for aleph_omega to destroy cofinal sparse families in ([\aleph_\omega]^\omega, \subseteq) and discuss how much sparseness we can get in ZFC for cofinal subfamilies of this partial order."]]><![CDATA[NO SEMINAR TODAY (University closed)]]>Mon, 27 Oct 2014 13:27:07 GMThttp://www.santispadaro.com/pcf-abstracts/no-seminar-todayNo seminar today, Monday, October 27 (university closed).]]><![CDATA[SPARSE FAMILIES AND THEIR APPLICATIONS]]>Mon, 20 Oct 2014 13:26:05 GMThttp://www.santispadaro.com/pcf-abstracts/sparse-families-and-their-applicationsSpeaker: 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."]]><![CDATA[CARDINAL ARITHMETIC AND REFLECTION THEOREMS FOR tHE LINDELOF DEGREE - NOTES BY ALBERTO LEVI]]>Sat, 18 Oct 2014 17:14:53 GMThttp://www.santispadaro.com/pcf-abstracts/cardinal-arithmetic-and-reflection-theorems-for-the-lindelof-degree-notes-by-alberto-leviHere are the notes prepared by Alberto Levi regarding his series of seminar lectures (29/09-12/10).]]><![CDATA[CARDINAL ARITHMETIC AND REFLECTION THEOREMS FOR THE LINDELOF DEGREE III]]>Tue, 14 Oct 2014 00:12:00 GMThttp://www.santispadaro.com/pcf-abstracts/cardinal-arithmetic-and-reflection-theorems-for-the-lindelof-degree-iiiDate 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."]]><![CDATA[CARDINAL ArithmetiC AND REFLECTION THEOREMS FOR THE LINDELOF DEGREE II.]]>Sun, 05 Oct 2014 20:56:09 GMThttp://www.santispadaro.com/pcf-abstracts/cardinal-arithmetic-and-reflection-theorems-for-the-lindelof-degree-iiDate 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.".]]><![CDATA[Cardinal arithmetic and reflection theorems for THE LindelĂ¶f degree]]>Mon, 29 Sep 2014 21:17:52 GMThttp://www.santispadaro.com/pcf-abstracts/reflection-of-lindelof-numberDate 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.".