** Set Theory Seminar**

** Friday, October 12, 2012, 10:00am GC 6417**

Speaker: Nam Trang

Title: GENERALIZED SOLOVAY MEASURES

Abstract: We will introduce some background and recent progress made

in solving the following open problem:

Determine the exact consistency strength of the theory T =

“ZF+DC+omega_1 is supercompact.”

It’s known that the upper-bound consistency strength for T is a class

of Woodin limits of Woodin cardinals which is (surprisingly) much

weaker than ZFC + a supercompact. We will discuss how one might go

about computing lower-bounds for T. If time allows, we’ll briefly talk

about the relationship of T with the Chang model (CM) and its

generalization (CM^+).

**Computational Logic Seminar**

** October 9, Time 2:00 – 4:00 PM, GC Room 3309.**

Speaker: Eugene Tyrtyshnikov, Russian Academy of Sciences

Title: New tensor decompositions in numerical analysis and data processing

Abstract: Tensor decompositions such as CANDECOMP/PARAFAC and Tucker’s

have been discussed for a long time. However, the main issues were

those connected with some algebraic varieties and fast matrix

multiplication algorithms, and, sometimes, other issues such as

Higher-Order SVD with a link to data processing. We consider some new

tensor decompositions such as TT (tensor trains) and HT (Hierarchical

Tucker) and the role they are beginning to play in matrix computations

and related problems of numerical analysis.

Both TT and HT decompositions are the results of one and same scheme

for the reduction of dimensionality. These decompositions are

frequently applied to tensors after some, often ultimate, quantization

of the original dimensions. This maximizes the number of modes and

makes the number of counts at each mode minimal possible, e.g. 2. We

consider how multilevel matrices become tensor trains with the use of

the Kronecker-product operation.

Then we show how new wavelet transforms arise in the construction of

tensor trains when forcing the TT ranks be limited. We also discuss

some examples and perspectives for applications.

In the end, we present an ambitious research goal of design of fast

tabulation procedures using a new interpolation instrument based a TT

generalization of the skeleton (dyadic) decomposition from matrices to

tensors.

REFERENCES

[1] I.Oseledets, E. Tyrtyshnikov, TT-cross approximation for multidimensional

arrays, Linear Algebra Appl., 432 (2010), pp. 70-88.

[2] I. Oseledets, E. Tyrtyshnikov, Algebraic wavelet transform via quantics

tensor train decomposition, SIAM J. Sci. Comp., vol. 31, no. 3 (2011),

pp. 1315-1328.

[3] I. Oseledets, E. Tyrtyshnikov, N. Zamarashkin, Tensor-train ranks for

matrices and their inverses, Comput. Meth. Appl. Math., Vol. 11, No. 3 (2011),

pp. 375-384.

**Model Theory Seminar**

** Fridays, October 12, 2012, 12:30pm-1:45pm, GC 6417**

Abhisekh Sankaran (IIT Bombay)

Preservation under Substructures modulo Bounded Cores

Abstract. We investigate a model-theoretic property that generalizes

the classical notion of preservation under substructures. We call this

property preservation under substructures modulo bounded cores, and

present a syntactic characterization via $\Sigma_2^0$ sentences for

properties of arbitrary structures definable by FO sentences. Towards

a sharper characterization, we show that the count of existential

quantifiers in the $\Sigma_2^0$ sentence equals the size of the

smallest bounded core, thus generalizing the classical Los-Tarski

theorem for sentences. We look at the notion of relativizations and

show its uses in establishing the sharper characterization for special

fragments of FO and also over special classes of structures. As a

fallout of our studies, we obtain combinatorial proofs of the

Los-Tarski theorem for some of the aforementioned cases.

**Logic Workshop**

** Friday, October 12, 2012 2:00 pm GC 6417**

Dr. Maryanthe Malliaris (University of Chicago)

Cofinality spectrum theorems in model theory, set theory, and general topology

**Seminar in Logic and Games**

** Friday, October 12, 2012, 4:15 PM, Room 6496**

Peter Godfrey-Smith (CUNY Graduate Center)

“Communication and Common Interest.”

Abstract: The stability of informative and cost-free signaling

requires common interest between sender and receiver. But what kind

and how much?

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