Daniel Rodriguez: Uniqueness of Supercompact measures III

Mathematical logic seminar – March 3, 2015
Time:     12:30 – 13:30

Room:     Wean Hall 8201

Speaker:         Daniel Rodriguez
Department of Mathematics
CMU

Title:     Uniqueness of Supercompact measures III

Abstract:

Assuming that there are ω-squared many Woodin cardinals with a measurable above them, we will continue the outline of the proof of the uniqueness of the models of the form L(ℝ,μ) that satisfy the theory “ZF+AD+ μ is an ℝ-supercompact measure”. If time permits we will discuss other scenarios and results.

Samuel Coskey: introduction to continuous logic

Wednesday, March 4 from 3 to 4pm
Room: Math 124
Speaker: Samuel Coskey (BSU)
Title: An introduction to continuous logic

Abstract: Continous logic is a proper generalization of first order logic where the usual binary truth values are replaced by the unit interval $[0,1]$. The models for this logic are metric structures, which are metric spaces together with continuous functions and $[0,1]$-valued relations. Just as ordinary logic has typical applications in discrete math, continuous logic has applications in analysis. In this talk we will introduce just the basic concepts and theory of continuous logic.

Szymon Żeberski: An example of a capacity for which all positive Borel sets are thick

Tuesday, March 3, 2015, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Szymon Żeberski (Wrocław University of Technology)

Title: An example of a capacity for which all positive Borel sets are thick

Abstract:

The result is obtained together with Michał Morayne. We will show an example of a capacity on Cantor’s cube for which all positive Borel sets can be partitioned into continuum many positive Borel sets.

Frank Tall: Some observations on the Baireness of C_k(X) for a locally compact space X

Place: Fields Institute, Room 210
Date and time: Friday 27 February 2015 (13:30-15:00)
Speaker: Frank Tall

Title: Some observations on the Baireness of C_k(X) for a locally compact space X

Abstract: The area in-between Empty not having a winning strategy and Nonempty having a winning strategy in the Banach-Mazur game has attracted interest for many decades. We answer some questions Marion Scheepers asked when he was here last year, and also prove results related to his recent  paper with Galvin and to a paper of Gruenhage and Ma. Our tools include PFA(S)[S] and non-reflecting stationary sets.

Jonathan Verner: Dynamical systems on ω* and weak-P-points

Wednesday, March 4, 2015, 11:00
Prague – IM AS CR, Zitna 25, seminar room, front building, third floor

Speaker: Jonathan Verner (Faculty of Philosophy and Arts, Charles University in Prague)

Title: Dynamical systems on ω* and weak-P-points

Ralf Schindler: Martin’s Maximum, Woodin’s (*), or both?

Friday Set Theory Seminar (HUJI)

We shall meet on February 27th (this Friday) in the Hebrew University
math department building in Room 110, at 10 am.

Speaker: Ralf Schindler (Münster)

Title:  Martin’s Maximum, Woodin’s (*), or both?

Abstract:  There are two plausible strong axioms available on the market
which both imply that there are $\aleph_2$ reals, Martin’s Maximum
and Woodin’s (*). It is still unknown if these two are compatible with
each other; this question leads to studying apparently unrelated issues
from descriptive inner model theory. We will present some joint
work with D. Aspero and H. Woodin.

Daniel Rodriguez: Uniqueness of Supercompact measures II

Mathematical logic seminar – February 24, 2015
Time:     12:30 – 13:30

Room:     Wean Hall 8201

Speaker:         Daniel Rodriguez
Department of Mathematics
CMU

Title:     Uniqueness of Supercompact measures  II

Abstract:

ADℝ is a natural strengthening of AD, which states that all games on real numbers are determined. Solovay proved that under ADℝ there is a canonical fine, normal countably complete measure on Pω1(ℝ) (we will call such measures ℝ-supercompact). Moreover Woodin showed that the models of the form L(ℝ,μ) satisfying the theory “ZF+AD+ + μ is an ℝ-supercompact measure” satisfy as well “μ is the unique such measure”. In recent work with Nam Trang, we proved that (modulo some large cardinals) the models of the form L(ℝ, μ) are unique (very much as Kunen’s version of L[U]). I will give the outline of the mentioned results of Solovay, and Woodin, and discuss the proof of the uniqueness of such models.

Postdoctoral position in set theory, Sao Paolo (Brazil)

Dear colleague,

We would like to announce a post-doctoral position in the Departament of
Mathematics of the University of São Paulo (Brazil) within the scope of
the set-theoretic aspects of Banach spaces and related structures, to work
in a joint project of Christina Brech and Piotr Koszmider (IM PAN, Warsaw)
who will spend 3 months each year in São Paulo during the project.
This position is for a period of 12 months, starting between April and September 2015.

Candidates interested in related fields such as applications of forcing in
analysis or set-theoretic aspects of C*-algebras, or planning to develop
their interests in these directions are welcome. The extended group
includes Valentin Ferenczi, Eloi Medina Galego and Artur Tomita and other
postdocs such as Dana Bartosova and Brice Mbombo.

The postdoc has no teaching duties and will receive a modest monthly
stipend of BRL 4100,00 (tax free). It also comprehends partial travel
support and BRL 4100,00 as a support for the first expenses upon arrival,
besides some small amount of money for traveling. These values should be
compatible with a modest life in São Paulo, for example sharing an
apartment close to a trendy neighborhood or renting an individual studio
in regular neighborhood close to the campus.

The candidates must have obtained their PhD not more than 7 years before
the starting date of the position and must submit their CV together with
the name and e-mail address of two people who could give a recommendation
letter to brech@ime.usp.br by March 15th.
For further information about this position, please send us a message at brech@ime.usp.br or p.koszmider@impan.pl.

We kindly ask you to forward this message to anyone you know that might be
interested in this position.

All the best,
Christina and Piotr

Daniel Rodriguez: Uniqueness of Supercompact measures I

Mathematical logic seminar – February 17, 2015
Time:     12:30 – 13:30

Room:     Wean Hall 8201

Speaker:         Daniel Rodriguez
Department of Mathematics
CMU

Title:     Uniqueness of Supercompact measures I

Abstract:

ADℝ is a natural strengthening of AD, which states that all games on real numbers are determined. Solovay proved that under ADℝ there is a canonical fine, normal countably complete measure on Pω1(ℝ) (we will call such measures ℝ-supercompact). Moreover Woodin showed that the models of the form L(ℝ,μ) satisfying the theory “ZF+AD+ + μ is an ℝ-supercompact measure” satisfy as well “μ is the unique such measure”. In recent work with Nam Trang, we proved that (modulo some large cardinals) the models of the form L(ℝ, μ) are unique (very much as Kunen’s version of L[U]). I will give the outline of the mentioned results of Solovay, and Woodin, and discuss the proof of the uniqueness of such models.

Randall Holmes: Preliminaries for Proving the Consistency of NF

Wednesday, February 11 from 3 to 4pm
Room: Math 124
Speaker: Randall Holmes (BSU)
Title: Preliminaries for Proving the Consistency of NF

Abstract: We will discuss some preliminary machinery intended for use in a consistency proof of Quine’s set theory New Foundations.
No particular familiarity with New Foundations is presupposed.