# This Week in Logic at CUNY

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