Friday, June 28, 10:00, room 201, the math building.
Speaker: Uri Abraham
Topic: In Solovay's model all linear operators on a Hilbert space are bounded - a description of a result of M. Wright
Abstract:
Friday, June 7, 10:00, room 201, the math building.
Speaker: Wieslaw Kubis
Topic: On the Wijsman topology
Abstract: The Wijsman topology on the space of closed subsets of given metric space is, by definition, the topology of pointwise convergence, after identifying a closed set A with its distance function dist(-,A). We will describe some properties of the Wijsman topology and its relations to other hyperspace topologies.
Friday, May 31, 10:00, room 201, the math building.
Speaker: Grigory Mashevitzky
Topic: A. Klein's rules of inference for implicational logic
Abstract: First we shall discuss the existence of maximal homomorphic images (replicas) of any algebra $A$ in any quasivariety $Q$, namely (the following invented by A.I. Malcev, characteristic property of quasivarieties: for any algebra $A$ and for any quasivariety $Q$ a quotient algebra of $A$ (replica) $A'\in Q$ exists such that for any quotient algebra $B$ of $A$, belonging to $Q$, $B$ is a quotient algebra of $A'$). Further we shall discuss the idea of R.W. Quackenbush of applying of the above property for obtaining rules of inference for implicational logic. Finally we use these ideas for discussion on A. Klein's rules of inference for implicational logic.
Friday, May 24, 10:00, room 201, the math building.
Speaker: Tomek Bartoszynski (Boise, USA)
Topic: Around the Borel conjecture
Abstract:
Friday, May 17, 10:00, room 201, the math building.
Speaker: Grigory Mashevitzky
Topic: On relatively free profinite semigroups
Abstract: In this introductory talk we discuss the role of profinite topology in the theory of pseudovarieties of groups and semigroups.
Pseudovariety of semigroups is a class of semigroups closed under homomorphic images, subsemigroups and finite direct products. Not any pseudovariety is the finite trace of a variety. Theorem of Reiterman states the analog of Birkhoff theorem, defining pseudoidentities as an equality of implicit operations-elements of free profinite semigroups.
Friday, May 3, 10:00, room -101, the math building.
Speaker: Grigory Mashevitzky
Topic: Some well known problems on quasiidentities
Abstract: In this introductory talk we plan to discuss some classical problems on quasiidentities. Particularly:
Let class $K$ of algebras be a prevariety, that is $K$ is defined by universal implications (may be infinite). For which $K$ it can be defined by quasiidentities ($K$ is a quasivariety) (A. I. Maltsev).
The decidability of the quasiequational theory and the uniform word problem (A. H. Mekler, E. Nelson, S. Shelah)
The conjecture of A. Klein on the consequencies of a system of quasiidentities.
Friday, April 19, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: Polarized chain conditions II
Abstract:
Friday, April 12, 10:00, room -101, the math building.
Speaker: Stefan Geschke (Free University, Beriln)
Topic: Covering R^n by continuous functions
Abstract:
Friday, April 5, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: Polarized chain conditions II
Abstract: Joint work with Saharon Shelah.
Friday, March 22, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: Polarized chain conditions
Abstract: Joint work with Saharon Shelah.
Friday, February 15, 10:00, room -101, the math building.
Speaker: Istvan Juhasz (Budapest)
Topic: Calibers, free sequences and density
Abstract: Results from a joint work with Z. Szentmiklossy. Below you can download the DVI, PS and PDF file.
Friday, January 11, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: On Borel sets VI
Friday, January 4, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: On Borel sets V
Friday, December 28, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: On Borel sets IV
Friday, December 21, 10:00, room -101, the math build$
Speaker: Uri Abraham
Topic: On Borel sets III
Friday, December 14, 10:00, room -101, the math building.
Speaker: Robert Bonnet (Universite de Savoie, France)
Topic: On well-generated Boolean algebras II
Friday, December 7, 10:00, room -101, the math building.
Speaker: Robert Bonnet (Universite de Savoie, France)
Topic: On well-generated Boolean algebras
Abstract: [DVI] [PDF] Let $B$ be a Boolean algebra. $B$ is well-generated if $B$ contains a well-founded (that is with no strictly decreasing infinite sequence) sublattice generating $B$.
The class of well-generated Boolean algebras plays the role of well-founded posets in the class of partially ordered sets.
For instance, the interval algebra $B(\alpha)$ of an ordinal $\alpha$ is well-generated. In fact every subalgebra of $B(\alpha)$ is well-generated.
Let $\alpha,\beta$ be two ordinals. $B^{\alpha\times\beta}$ denotes the free product of the interval algebras $B(\alpha)$ and $B(\beta)$. We can identify $B^{\alpha\times\beta}$ with the subalgebra of subsets of $\alpha\times\beta$ formed by all finite unions of rectangles of the form $[\gamma,\delta)\times[p,q)$, where $p<q\leq\alpha$ and $\gamma<\delta<\beta$.
In that case, the situation is different.
For instance $B^{\aleph_1\times\aleph_1}$ contains a non well-generated subalgebra.
But every subalgebra of $B^{\aleph_1\times\aleph_0}$ is well-generated.
Friday, November 23, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: On Borel sets II
Abstract: A series of lectures about Borel sets, culminating in Martin's theorem about the determinacy of Borel games. These lectures are intended not only to specialists in set theory.
Friday, November 16, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: On Borel sets
Abstract: A series of lectures about Borel sets, culminating in Martin's theorem about the determinacy of Borel games. These lectures are intended not only to specialists in set theory.
Friday, October 26, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: $\aleph_1$-dense subsets of the reals.
Friday, July 13, 10:00, room -101, the math building.
Speaker: Arkady Leiderman
Topic: Uniquely homogeneous topological spaces
Tuesday, July 10, 11:00, room 201, the math building.
Speaker: Matti Rubin
Topic: Ohkuma structures (part 6)
Abstract:
Friday, July 6, 10:00, room -101, the math building.
Speaker: Grigory Mashevitzky
Topic: Universal algebraic geometry and automorphisms of categories of free algebras
Abstract:
Tuesday, July 3, 11:00, room 102, building 38 (?).
Speaker: Matti Rubin
Topic: Ohkuma structures (part 5)
Abstract:
Friday, June 29, 10:00, room 201, the math building.
Speaker: Grigory Mashevitzky
Topic: The finite basis problem
Abstract:
Tuesday, June 26, 11:00, room 201, the math building.
Speaker: Matti Rubin
Topic: Ohkuma structures (part 4)
Abstract:
Friday, June 22, 10:00, room -101, the math building.
Speaker: Matti Rubin
Topic: Ohkuma structures (part 3)
Abstract:
Friday, June 15, 10:00, room -101, the math building.
Speaker: Matti Rubin
Topic: Ohkuma structures (part 2)
Abstract:
Friday, June 8, 10:00, room -101, the math building.
Speaker: Matti Rubin
Topic: Ohkuma structures
Abstract:
Tuesday, June 5, 11:00, room 201, the math building.
A guest lecture on ordered groups III.
Speaker: Professor Charles Holland, Bowling Green State University, Ohio. (Dozor Fellow).
Topic: The varieties of lattice ordered groups.
Abstract: The varieties (equational classes) of lattice-ordered groups which cover the variety the abelian lattice ordered groups form a rich area of investigation which is not completely understood. There are exactly countably many varieties of solvable lattice ordered groups which are covers, and each of these is known. In this seminar, we will investigate the non-solvable covers. Each of these is generated by a totally ordered free group. For a large collection (continuum many), the ordering of the free group is associated with an infinite sequence of -1's and +1's which is minimal in a certain topological sense. We will describe the connection, and raise the question, open for many years now, of whether there are other covers.
Friday, June 1, 10:00, room -101, the math building.
A guest lecture on ordered groups.
Topic: Embedding ordered groups in divisible ordered groups.
Abstract: It is an open question whether every ordered group is embeddable in a divisible ordered group. The speaker will describe the known results in this topic: There is a positive answer for abelian and even nilpotent ordered groups, and for Archimedean rank 2 ordered groups. The question is open even for Archimedean rank 3 ordered groups.
Tuesday, May 29, 11:00, room 201, the math building.
A guest lecture on ordered groups
Topic: Structures with a uniquely transitive automorphism group.
Abstract: The automorphism group of a structure is said to be uniquely transitive, if for every x and y in the structure there is a unique automorphism of the structure taking x to y. The existence of ordered structures with this property will be proved. This property of the automorphism group will be also discussed for graphs and for circular orders.
Friday, May 11, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: Polarized chain conditions
Abstract:
Tuesday, May 1, 11:00, room 201, the math building.
Speaker: Uri Abraham
Topic: Polarized chain conditions
Abstract:
Tuesday, April 24, 11:00, room 201, the math building.
Speaker: Wieslaw Kubis
Topic: On supercompact spaces
Abstract: We present some examples of supercompact and non-supercompact topological spaces.
Friday, April 20, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: aleph_1 - dense subsets of reals (continuation)
Abstract:
Tuesday, April 10, 11:00, room 201, the math building.
Speaker: Wieslaw Kubis
Topic: On supercompact spaces (the sequel)
Abstract: See [here].
Tuesday, April 3, 11:00, room 201, the math building.
Speaker: Wieslaw Kubis
Topic: On supercompact spaces (the continuation)
Friday, March 30, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: aleph_1 - dense subsets of reals
Abstract:
Tuesday, March 27, 11:00, room 201, the math building.
Speaker: Wieslaw Kubis
Topic: On supercompact spaces
Abstract: A topological space is supercompact if it has a binary subbase for closed sets; a collection of sets is binary if any its subcollection with empty intersection contains two disjoint elements. The notion of supercompactness was introduced by de Groot in 1967. He conjectured that all metric compacta are supercompact, which was later proved by Strok and Szymanski in 1975. Not all compact spaces are supercompact: e.g. an infinite supercompact space contains nontrivial convergent sequences. Also, there exists a first countable compact space of weight aleph_1 which is not supercompact.
We will present a short and elementary proof of the theorem of Strok-Szymanski.
Friday, March 23, 10:00, room -101, the math building.
Speaker: Uri Abraham
Topic: Chain conditions in free products of Boolean algebras
Abstract: There exist in ZFC two Boolean algebras satisfying the \aleph_{\omega+1} chain condition such that their free product fails to satisfy the \aleph_{\omega+1} chain condition.
