HUJI Logic Seminar
16/Jan/2019, 11-13, Ross 63.
Speaker: Menachem Magidor
Title: Omitting types in the logic of metric structures
(joint work with I. Farah)
The logic of metric structures was introduced by Ben Yaacov, Berenstein , Henson and Usvyatsov. It is a version of continuous logic which allows fruitful model theory for many kinds of metric structures. There are many aspects of this logic which make it similar to first order logic, like compactness, a complete proof system, an omitting types theorem for complete types etc. But when one tries to generalize the omitting type criteria to general (non-complete) types the problem turns out to be essentially more difficult than the first order situation. For instance one can have two types (in a complete theory) that each one can be omitted, but they can not be omitted simultaneously.
In the beginning of the talk we shall give a brief survey of the logic of metric structures, so the talk should be accessible also the listeners who are not familiar with the logic of metric structures.
BIU Infinite Combinatorics Seminar
Date : 31/12/2018 – 13:00 – 15:00
Speaker: Miguel Moreno (BIU)
Title : An introduction to generalized descriptive set theory, part 2
Abstract. After introducing the notions of $\kappa$-Borel class, $\kappa$-$\Delta_1^1$ class, $\kappa$-Borel^* class in the previous talk, in this talk, we will show the relation between this classes.
In descriptive set theory the Borel class, the $\Delta_1^1$ class, the Borel* class are the same class, this doesn’t hold in the generalized descriptive set theory, in particular under the assumption V=L the Borel* class is equal to the $\Sigma1^ 1$ class.
TAU Forcing Seminar
Speaker: Matt Foreman
Title: Games on weakly compact cardinals
Colloquium, Hebrew University of Jerusalem
Thu, 20/12/2018 – 14:30 to 15:30
Manchester Building (Hall 2), Hebrew University Jerusalem
Speaker: Assaf Rinot
Title: Hindman’s theorem and uncountable Abelian groups
Abstract. In the early 1970’s, Hindman proved a beautiful theorem in additive Ramsey theory asserting that for any partition of the set of natural numbers into finitely many cells, there exists some infinite set such that all of its finite sums belong to a single cell. In this talk, we shall address generalizations of this statement to the realm of the uncountable. Among other things, we shall present a negative partition relation for the real line which simultaneously generalizes a recent theorem of Hindman, Leader and Strauss, and a classic theorem of Galvin and Shelah. This is joint work with David Fernandez-Breton.
BIU seminar in Set Theory
December 17, 2018
Speaker: Asaf Karagila (UEA)
Title: On countable unions of countable sets
Abstract. How big can countable unions of countable sets be? Assuming the axiom of choice, countable. Not assuming the axiom of choice, it is not hard to arrange situation where there are many incomparable cardinals which are the countable union of countable sets. But none of them are “particularly large”. While a countable union of countable sets can at most be mapped onto $\omega_1$, its power set can be made much larger. We prove an old (and nearly forgotten) theorem of Douglass Morris, that it is consistent that for every $\alpha$ there is a set which is a countable union of countable sets, but its power set can be mapped onto $\alpha$.
HUJI Logic Seminar
12/December/18, 11 am, in Ross 63.
Speaker: Ilijas Farah
Title: On the model theory of C*-algebras
Abstract. Ultrapowers and reduced products play a central role in the Elliott classification program for separable (nuclear, etc.) C*-algebras. Although an ultrapower of a separable C*-algebra A is quite different from the reduced product ℓ∞(A)/c0(A)
, these massive algebras are interchangeable in many (but not quite all) concrete applications. I will present a theorem
that attempts to give an abstract explanation of this phenomenon. This preliminary result applies to some other axiomatizable categories, and its proof does not use any of the nontrivial theory of C*-algebras.
No previous knowledge of C*-algebras is required; they appear primarily as a motivation.
This is preliminary part of a joint work with Christopher Schafhauser.
HUJI Logic Seminar
21 November 2018
Speaker: Saharon Shelah
Title: The spectrum of the existence of a universal model
Abstract. The existence of a universal model (of a theory T in a cardinal lambda) is a natural question in model theory and set theory. We shall deal with new sufficient conditions for non-existence.
HUJI Set Theory Seminar
November 14, 2018
Speaker: Shimon Garti
Abstract. We shall try to prove the consistency of d_lambda > r_lambda (and even d_lambda > u_lambda) for a singular cardinal lambda.
This is a joint work with Saharon.